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Reliable Multicast Transport                                E. Stauffer
Internet Draft                                                 Broadcom
                                                                B. Shen
                                                               Broadcom
                                                         S. Chakraborty
                                                               Broadcom
                                                            D. Tujkovic
                                                               Broadcom
                                                               J. Huang
                                                               Broadcom
                                                                S. Shet
                                                               Broadcom
                                                                K. Rath
                                                               Broadcom
Intended status: Standards Track                         March 29, 2014
Expires: September 2014



                            Supercharged Codes
               draft-stauffer-rmt-bb-fec-supercharged-04.txt


Status of this Memo

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   This Internet-Draft will expire on September 27, 2014.






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Copyright Notice

   Copyright (c) 2012 IETF Trust and the persons identified as the
   document authors. All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
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   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Abstract

This document describes a fully-specified FEC scheme for the
Supercharged forward error correction code.  Supercharged codes are
designed for use on the erasure channel.  Coding for the erasure
channel commonly arises for data transmission over the internet, where
lower layers either successfully deliver packets or fail to deliver
them.  Coding is required to insure that data is not lost, even if
packets are lost at the lower layers.  Error free reception is
important for multimedia applications, such as streaming, where it may
not be possible to correct an error in time by any other means.  Coding
insures that lost packets can be recovered.

Table of Contents


   1. Introduction...................................................3
   2. Supercharged Code..............................................3
         2.1.1. Definitions..........................................3
      2.2. Overview..................................................4
      2.3. Matrix Representation.....................................5
      2.4. Systematic Encoding.......................................6
      2.5. Erasure Channel...........................................6
      2.6. Decoding..................................................7
      2.7. Matrix P Construction.....................................7
         2.7.1. Function Prototypes..................................7
         2.7.2. Parallel Filter Code T Construction..................8
         2.7.3. Repetition Code R Construction......................10
         2.7.4. Block Code B_1 Construction.........................11
         2.7.5. Block Code B_2 and B_3 Construction.................11
         2.7.6. SC_Parameters.......................................13
         2.7.7. K Table.............................................13


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         2.7.8. Random Number Generator.............................18
         2.7.9. Random Permutation..................................22
         2.7.10. RS Generator.......................................23
         2.7.11. RS Code............................................24
         2.7.12. SC_Filter_Data.....................................24
         2.7.13. GF(256) Operations.................................25
   3. FEC Packets...................................................25
      3.1. Segmentation.............................................25
         3.1.1. Transmit Blocks.....................................25
         3.1.2. Working Blocks......................................26
         3.1.3. Padding.............................................26
   4. Parameter Selection...........................................26
   5. Control Messages..............................................27
      5.1. FEC Payload ID...........................................27
      5.2. FEC Object Transmission Information......................27
         5.2.1. FEC Encoding ID.....................................27
         5.2.2. Common..............................................27
         5.2.3. Scheme Specific.....................................28
   6. Conventions used in this document.............................29
   7. Security Considerations.......................................29
   8. IANA Considerations...........................................29
   9. References....................................................29
      9.1. Normative References.....................................29
      9.2. Informative References...................................29
   10. Acknowledgments..............................................30

1. Introduction

   This document describes a fully-specified FEC scheme for the
   Supercharged forward error correction code.  The Supercharged code is
   designed for the erasure channel with performance very close to the
   ideal Maximum Distance Separable(MDS) code and with very low
   complexity.  Section 2 describes the architecture of the code and
   defines the generator matrices used by the code.  Section 3 describes
   how to construct FEC packets.  Section 4 discusses code parameter
   selection for a particular usage context.  Section 5 defines the
   protocol information elements.  Section 6 considers security.
   Section 7 considers IANA.

2. Supercharged Code

2.1.1. Definitions

   ceil(a): rounds a to the nearest integer towards infinity

   floor(a): rounds a to the nearest integer towards minus infinity



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   min(a,b): returns the minimum of a and b

   max(a,b): returns the maximum of a and b

   a % b: is a modulo b

   a + b: is a plus b

   a * b: is a multiplied by b.

   a ^ b: the bitwise XOR of a and b

   a ^^ b: raises a to the b power

   I_a: the a x a identity matrix

   zeros(a,b): the a x b zero matrix

2.2. Overview

   Figure 1 shows a general block diagram of the supercharged code.  It
   consists of a network of codes including block codes, repetition
   codes, and parallel filter codes.  Block code 1 consists of a
   Vandermonde matrix in GF(256), a non-systematic Reed Solomon code.
   Block code 2 and 3 consist of binary block codes.


            +--------------+   +-----------------+
        +---| Block Code 1 |---| Repetition Code |---+
        |   +--------------+   +-----------------+   |
        |                                            |
        |   +--------------+   +-----------------+   |
   x ---+---| Block Code 2 |---| Repetition Code |---+----- y
        |   +--------------+   +-----------------+   |
        |                                            |
        |   +--------------+   +-----------------+   |
        +---| Block Code 3 |---|                 |   |
        |   +--------------+   |                 |   |
        |                      | Parallel Filter |---+
        +----------------------|      Code       |
                               |                 |
                               +-----------------+

             Figure 1  Block Diagram of the SC Code





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   The parallel filter code of Figure 1 is detailed in Figure 2.  It
   consists of interleavers, tailbiting FIR filters, and a multiplexer
   to select the output of the filters.

                              +----------------+
          +---------------+   | Tailbiting FIR |
      +---| Interleaver 1 |---|     Filter     |-------+
      |   +---------------+   |                |       |
      |                       +----------------+    +-----+
   ---+         ...                  ...            | Mux |---
      |                       +----------------+    +-----+
      |   +---------------+   | Tailbiting FIR |       |
      +---| Interleaver M |---|     Filter     |-------+
          +---------------+   |                |
                              +----------------+

             Figure 2  An example parallel filter code showing
             individual data interleavers and tailbiting FIR filters as
             coding components.

   An example of one of the tailbiting FIR filters is illustrated in
   Figure 3, where the state of the filter is initialized with the final
   state to make it tailbiting.



                          +---+   +---+   +---+
                       ---| D |---| D |---| D |
                          +---+   +---+   +---+
                            |       |       |
                            +-------+-------+
                                    |
                                    +--------------

             Figure 3  An example 3 tap FIR filter that can be used for
             the tailbiting FIR filter coding component.  An XOR
             operation is applied at the output of the delay elements
             to produce the final output.

   Optionally, if the number of transmit symbols N is signaled to be
   limited such that N<=256, then the code can achieve ideal performance
   by utilizing a Reed Solomon code.

2.3. Matrix Representation

   Since supercharged codes are linear, an output codeword can be
   expressed as a matrix multiplied by an input vector.  Given Kx1


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   encoding state vector x, consisting of binary transmit symbols, the
   output Nx1 codeword, y, can be written as

                   y = (T*[I_K; B_3] + R_1*B_1 + R_2*B_2)*x          (1)

   where T is the N x (K+Num_B_3) generator matrix for the FIR
   structure, B_1 is the Num_V_RS x K generator matrix for the first
   block code, B_2 is the Num_B_2 x K generator for the second block
   code, B_3 is the Num_B_3 x K generator matrix of the third block
   code, and R_1 is a N x Num_V_RS stack and R_2 is a N x Num_B_2 stack
   of identity matrices which facilitates repetition.  For example,
   matrix R_1 would consist of floor(N/Num_V_RS) copies of the identity
   matrix stacked vertically, with a fractional identity matrix below
   consisting of N mod Num_V_RS rows.  The "+"operator indicates the
   bitwise XOR operation.  For convenience, denote the generator matrix
   P = (T*[I_K; B_3] + R_1*B_1 + R_2*B_2), such that y=Px.

2.4. Systematic Encoding

   Supercharged codes are not inherently systematic codes.  Non-
   systematic codes are commonly transformed into an effective
   systematic code by pre-processing the input data before using it as
   the input to the encoder, y=Px.  The encoder input is calculated by
   decoding the desired input data and running the decoder to determine
   the encoder input vector x.  Let matrix P_enc be the KxK generating
   matrix corresponding to the first K elements of y, the encoder input
   x can be computed using the following

                          x = P_enc^^(-1) * d.

   Now, x can be used to encode using equation (1) to generate y.  The
   first K elements of vector y will be equal to d.

2.5. Erasure Channel

   After encoding, the N transmit symbols of codeword vector y are
   transmitted on the channel.  Some of these transmit symbols are
   erased by the channel.  Suppose that the Nxr matrix E represents the
   erasure pattern of the channel in that it selects out the r received
   transmit symbols y_r from the transmitted symbols y.  If the ith
   received symbol is the jth transmit symbol, then E(i,j)=1.  This
   results in

                              y_r = E*y.

   At the decoder, the effective generator matrix at the receiver is P_r
   = E*P.


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2.6. Decoding

   Decoding is the process of determining x given y_r and P_r.  Decoding
   can be implemented in several different ways, but each are equivalent
   to solving the least squares problem x = (P_r^^T*P_r)^^-1 * P_r^^T *
   y_r.  Modern sparse matrix factorization techniques can take
   advantage of the sparse structure imposed by the parallel filter
   structure if (1) is rewritten in the following equivalent form

                                z = Gw,                              (2)

   with augmented generator matrix G defined as

                   G = [ [B_3; B_2; B_1] I_L; T R_2 R_1]

   and where the augmented output vector z=[zeros(L,1); y], the
   augmented input vector w=[x; B_3*x; B_2*x; B_1*x], and where L=
   Num_V_RS+Num_B_2+Num_B_3.  The bottom L elements of vector w contain
   the outputs, before repetition, of the block codes.  These L values
   are appended to vector x to form the augmented input vector w.  The
   first L rows of G implement the block code and XOR the block code
   output with itself to generate the L zeros at the top of the z
   vector.  The subsequent N rows of G implement the FIR structure and
   XOR the output with the output of the block codes.

   This problem can be efficiently solved using direct sparse matrix
   factorization techniques described in [3-8].  It is RECOMMENDED that
   the Dulmage-Mendelsohn based solver in chapter 8 of [5] be used with
   addition, multiplication, and division updated to support a finite
   field.  This algorithm utilizes pivoting based on node degrees in the
   equivalent graph to minimize fill-in.  The solution is completed by
   performing forward and backward substitutions.  Iterative solvers are
   also possible.

   Once the encoder state vector x, or equivalently the augmented
   encoder state vector w, has been determined, the task remains to
   determine the data vector d.  For any elements of d that are missing,
   then can be recovered by using appropriate rows of (1) or (2).



2.7. Matrix P Construction

2.7.1. Function Prototypes

   The following functions are utilized to construction the Supercharged
   code.


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   [K_eff, Num_V_RS, Num_B_2, Num_B_3] = SC_Parameters(K, N)

   K_eff=SC_K_table(K)

   b=RNG(a)

   a=RNG_2(a,b)

   [permutation,the_seed]= Generate_Permutation(a,b)

   G_V_RS = RS_gen(K,N)

   [filter_data, filter_N]=SC_filter_data(z)

   b=GF_exp(a)

   C=GF_Multiply(A,B)



2.7.2. Parallel Filter Code T Construction

   The parallel filter code matrix T can be generated using the
   following pseudo code.  The code generates multiple random
   interleavers and selects which output of which interleaver depending
   on the SID, where the SID is definded in section 3.   Note that at
   the receiver, only filter outputs corresponding to the received SID's
   are required.  The following code generates filter outputs for SIDs 0
   to N-1.  Determination of the filter output is a function of the SID
   only, not any other filter output, making it simple to generate only
   the filter outputs needed at encoding or decoding. The
   Generate_Permutation function is defined in section 2.7.9. , the
   SC_filter_data function is defined in section 2.7.12. , and the RNG
   function is defined in section 2.7.8.

       seed1 = 758492

       seed2 = ( (K_eff*874) ^ (seed1) )

       seed3 = 23091

       base_permutation = Generate_Permutation(K_eff+Num_B_3,seed2)

       filter_data = SC_filter_data(K_eff+Num_B_3)





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       T = zeros(N,K_eff+NUM_B_3)

       for SID=0:N-1

           %Determine which filter to select

           rn1 = min( RNG(15*(SID+1)+2*seed3) , 2^^32 )

           index = 0

           while(rn1>(filter_data[index]))

                index = index+1

           end



           tdeg=index+1



           %Determine which interleaver to select

           rn2 = min( RNG(2*K_eff+3*(SID+1)) , 2^^32 )

           interleaver_number = ( (rn2) % (K_eff+Num_B_3) )



           %Determine which part of the interleaver to select

           rn3 = min( RNG(98573+2*(SID+1)+rn1) , 2^^32 )

           interleaver_part = ((rn3) % (K_eff+Num_B_3))



           for tap_loop=0:tdeg

               filter_tap = (tap_loop+interleaver_part) %
   (K_eff+Num_B_3)

               tap_location = (base_permutation[filter_tap] +
   base_permutation[interleaver_number]) % (K_eff+Num_B_3)

               T[Num_V_RS+Num_B_2+Num_B_3+SID,tap_location] = 1


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           end

       end


2.7.3. Repetition Code R Construction

   The repetition code matrix R_1 and R_2 can be constructed via the
   following pseudo code.  Note that at the receiver, only filter
   outputs corresponding to the received SID's are required.  The
   following code generates filter outputs for SIDs 0 to N-1 for R_1.

      R_1 = zeros(N,Num_V_RS)

       for SID = 0:N-1

           for k = 0:Num_V_RS-1

               if( ((SID-k) % (Num_V_RS)) == 0 )

                   R_1[SID,k] = 1

               end

           end

       end


   The following code generates filter outputs for SIDs 0 to N-1 for
   R_2.

       R_2 = zeros(N, Num_B_2)

       for SID = 0:N-1

           for k = 0: Num_B_2-1

               if( ((SID-k) % (Num_B_2)) == 0 )

                   R_2[SID,k] = 1

               end

           end




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       end


2.7.4. Block Code B_1 Construction

   The Vandermonde matrix of block code B_1 can be constructed via the
   following pseudo code.  The GF_exp function is defined in section
   2.7.13.


        B_1 = zeros(Num_V_RS,K_eff)

       for i = 0:Num_V_RS-1

           for k = 0:K_eff-1

               B_1[i+1,k+1] = GF_exp( ((i+1)*k) % (2^^8-1) )

           end

       end



2.7.5. Block Code B_2 and B_3 Construction

   The block code B_2 and B_3 can be constructed jointly via the
   following pseudo code, where B_23=[B_3; B_2].


       B_23 = zeros(Num_B_2 + Num_B_3,K_eff)

       for i = 0:K_eff-1

           for k = 0: Num_B_2 + Num_B_3 - 1

               if( ( (k-i) % (Num_B_2 + Num_B_3) ) == 0)

                   B_23[k,i] = 1

               end

           end




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       end



       m=1

       for i = 0:K_eff-1

           for k = 0: Num_B_2 + Num_B_3 - 1

               if( ( (k-i-2*floor(m/( Num_B_2 + Num_B_3))) % (Num_B_2 +
   Num_B_3) ) == 0)

                   B_23[k,i] = 1

               end

               m = m+1

           end

       end



       m=2

       for i = 0:K_eff-1

           for k = 0: Num_B_2 + Num_B_3 - 1

               if( ( (k-i-3*floor(m/( Num_B_2 + Num_B_3))) % (Num_B_2 +
   Num_B_3) ) == 0)

                   B_23[k,i] = 1

               end

               m = m+1

           end


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       end




2.7.6. SC_Parameters

   The following pseudo code determines a set of parameters needed for
   matrix construction.  The SC_K_table is defined in section 2.7.7.

   function [K_eff, Num_V_RS, Num_B_2, Num_B_3] = SC_Parameters(K, N)

        K_eff = SC_K_table(K)

       Num_V_RS = 11 + floor(K_eff/10000)

       Num_B = floor(K_eff^^(0.62)) + 3

       if( K_eff >= 17376 )

           Num_B = ceil( K_eff*0.0152 + 163 )

       end

       Num_B_3 = ceil(0.75*( Num_B ))

       Num_B_2 = Num_B - Num_B_3





2.7.7. K Table

   The function K_eff=SC_K_table(K) is implemented based on the
   following table, by returning the smallest K_eff such that K_eff>=K.

   10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
   33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
   56,57,58,59,60,61,62,63,64,65,66,67,69,70,71,72,73,74,75,76,77,78,79,
   80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,1
   02,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,11
   9,120,121,122,123,124,125,126,127,128,129,130,131,133,134,135,136,137
   ,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,
   155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,1


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   72,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,18
   9,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206
   ,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,
   224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,2
   41,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,25
   8,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275
   ,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,
   293,294,295,296,297,298,299,300,302,303,304,305,306,307,308,309,310,3
   11,312,314,315,316,320,321,324,328,329,335,337,338,340,341,344,347,34
   9,352,355,357,358,360,362,364,366,368,372,377,380,381,382,384,385,388
   ,389,393,394,395,397,399,405,408,409,410,411,416,418,424,426,428,431,
   432,434,438,443,447,448,451,452,453,457,460,465,466,467,469,473,476,4
   77,478,482,483,484,485,486,490,491,492,493,494,496,497,498,500,501,50
   2,503,504,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520
   ,521,522,524,526,527,528,529,530,532,533,534,535,536,537,539,541,542,
   543,545,546,549,551,552,553,554,555,557,558,559,561,562,563,564,566,5
   69,571,572,573,574,576,577,578,579,580,582,583,585,586,587,588,589,59
   0,592,593,594,597,598,599,600,602,603,606,607,608,609,610,612,614,615
   ,616,617,619,620,622,625,626,627,628,629,630,631,633,635,636,637,638,
   640,643,645,648,650,652,653,654,655,656,659,660,661,662,664,666,667,6
   68,669,672,673,674,675,677,687,688,691,692,693,694,695,696,698,699,70
   0,701,703,710,711,712,715,716,717,718,726,727,730,731,734,736,737,741
   ,744,747,748,751,752,753,757,759,760,762,764,766,769,771,772,773,774,
   775,777,778,779,786,788,790,792,793,794,795,797,798,799,800,801,802,8
   04,805,810,811,812,813,815,820,821,822,823,825,827,829,830,831,834,83
   5,837,838,839,840,843,844,845,846,848,849,851,852,853,854,857,858,860
   ,863,864,866,868,869,870,875,877,879,883,886,887,890,891,894,897,898,
   899,900,902,903,904,905,906,907,909,912,913,914,917,922,926,927,928,9
   31,934,938,940,942,944,945,948,950,953,954,960,961,963,967,968,970,97
   1,972,974,977,979,980,981,985,987,989,990,995,996,1000,1002,1003,1005
   ,1006,1007,1009,1010,1015,1020,1021,1022,1024,1025,1027,1032,1033,103
   4,1035,1037,1041,1042,1043,1046,1048,1050,1051,1054,1056,1057,1059,10
   60,1062,1065,1069,1070,1071,1074,1076,1078,1079,1082,1083,1085,1086,1
   087,1088,1089,1095,1098,1099,1106,1110,1111,1118,1120,1123,1124,1125,
   1131,1132,1134,1136,1139,1140,1142,1144,1150,1152,1157,1161,1162,1165
   ,1169,1173,1175,1176,1179,1181,1182,1183,1194,1200,1201,1204,1205,120
   6,1208,1209,1212,1213,1214,1218,1219,1220,1222,1225,1227,1228,1229,12
   32,1236,1238,1240,1242,1243,1245,1248,1250,1252,1253,1255,1258,1261,1
   269,1273,1278,1279,1280,1283,1284,1292,1293,1302,1303,1306,1310,1311,
   1315,1318,1319,1321,1325,1330,1331,1342,1343,1347,1348,1352,1357,1359
   ,1361,1365,1374,1380,1382,1384,1388,1389,1390,1391,1392,1395,1397,140
   3,1404,1407,1413,1417,1418,1420,1425,1429,1431,1435,1436,1437,1447,14
   50,1461,1462,1464,1473,1474,1475,1477,1485,1490,1494,1496,1497,1502,1
   503,1507,1513,1514,1516,1521,1522,1526,1530,1534,1539,1541,1549,1552,
   1554,1555,1561,1564,1569,1572,1579,1585,1586,1590,1591,1593,1595,1596
   ,1597,1598,1600,1604,1608,1610,1611,1612,1616,1617,1624,1631,1633,163
   6,1641,1646,1649,1650,1658,1660,1665,1667,1671,1673,1679,1683,1689,16


Stauffer, et al.       Expires September 29, 2014              [Page 14]


Internet-Draft            Supercharged Code                   March 2014


   92,1696,1698,1703,1705,1707,1708,1713,1716,1722,1728,1733,1734,1739,1
   740,1742,1744,1745,1756,1759,1760,1764,1768,1771,1776,1777,1780,1782,
   1787,1800,1807,1814,1824,1826,1827,1842,1844,1854,1857,1863,1867,1873
   ,1874,1878,1881,1883,1887,1889,1890,1891,1892,1894,1896,1903,1905,190
   6,1910,1919,1924,1926,1931,1933,1943,1944,1948,1952,1954,1967,1971,19
   73,1976,1979,1985,1986,1987,1989,1992,1994,1995,1998,2000,2005,2006,2
   018,2019,2030,2040,2043,2048,2054,2055,2057,2061,2070,2071,2074,2077,
   2082,2084,2087,2089,2093,2096,2098,2103,2104,2107,2111,2120,2122,2125
   ,2128,2138,2150,2152,2155,2160,2175,2177,2182,2189,2195,2200,2201,220
   3,2217,2219,2225,2226,2231,2234,2235,2236,2237,2245,2247,2274,2276,22
   78,2280,2282,2283,2286,2292,2303,2304,2306,2310,2315,2316,2319,2320,2
   321,2330,2333,2336,2339,2343,2344,2345,2351,2367,2368,2371,2374,2382,
   2389,2392,2395,2396,2400,2402,2407,2410,2412,2416,2421,2422,2434,2442
   ,2446,2447,2462,2473,2477,2478,2481,2486,2490,2492,2495,2502,2505,250
   7,2509,2512,2513,2522,2525,2527,2528,2536,2543,2549,2556,2559,2561,25
   63,2565,2583,2587,2590,2592,2596,2598,2601,2603,2604,2606,2617,2622,2
   625,2626,2636,2638,2640,2643,2654,2660,2668,2673,2677,2679,2688,2695,
   2699,2701,2713,2714,2723,2737,2741,2747,2753,2762,2764,2769,2772,2775
   ,2776,2785,2796,2802,2805,2808,2826,2828,2830,2831,2834,2836,2853,287
   5,2877,2878,2884,2906,2938,2945,2948,2950,2961,2964,2966,2968,2979,29
   80,2985,2989,2998,3008,3011,3015,3018,3022,3027,3048,3049,3051,3053,3
   056,3062,3071,3075,3080,3093,3094,3095,3097,3101,3107,3109,3119,3122,
   3128,3149,3150,3151,3158,3166,3167,3173,3178,3180,3181,3182,3186,3190
   ,3195,3200,3201,3203,3204,3205,3208,3216,3217,3223,3224,3232,3236,324
   0,3248,3251,3253,3269,3276,3278,3279,3286,3292,3299,3306,3309,3336,33
   40,3342,3344,3351,3352,3356,3357,3371,3375,3380,3387,3396,3404,3407,3
   410,3423,3430,3445,3451,3463,3466,3471,3478,3479,3502,3513,3520,3528,
   3531,3534,3539,3540,3546,3551,3565,3577,3579,3603,3606,3608,3612,3614
   ,3616,3620,3647,3650,3653,3658,3664,3677,3682,3686,3694,3697,3705,370
   7,3724,3728,3744,3749,3751,3754,3761,3765,3776,3778,3781,3792,3797,37
   99,3801,3834,3840,3841,3848,3861,3863,3883,3901,3903,3919,3924,3941,3
   943,3960,3965,3970,3971,3989,3992,4007,4013,4015,4037,4039,4045,4050,
   4055,4069,4072,4073,4091,4096,4106,4112,4124,4129,4133,4140,4146,4156
   ,4165,4188,4207,4209,4210,4215,4221,4236,4237,4247,4252,4253,4257,426
   1,4266,4270,4318,4330,4341,4346,4359,4363,4365,4366,4388,4415,4418,44
   36,4438,4453,4468,4474,4477,4503,4512,4513,4519,4522,4538,4548,4567,4
   575,4576,4577,4583,4590,4621,4639,4651,4659,4681,4693,4698,4700,4702,
   4729,4731,4739,4741,4742,4748,4749,4758,4764,4765,4771,4772,4780,4785
   ,4803,4804,4838,4840,4843,4868,4871,4878,4885,4898,4901,4918,4924,493
   3,4939,4954,4959,4979,4982,4988,4991,4999,5000,5008,5021,5023,5030,50
   39,5060,5062,5063,5096,5116,5137,5143,5145,5162,5163,5167,5172,5186,5
   218,5225,5238,5240,5252,5260,5279,5285,5295,5301,5310,5314,5317,5331,
   5332,5334,5348,5353,5354,5390,5391,5392,5405,5407,5432,5449,5451,5453
   ,5460,5464,5466,5471,5473,5477,5492,5506,5508,5537,5540,5543,5554,556
   1,5566,5570,5576,5579,5587,5616,5637,5672,5674,5676,5684,5694,5716,57
   32,5774,5792,5798,5800,5808,5823,5838,5844,5863,5896,5897,5899,5900,5
   916,5921,5930,5960,5975,6039,6055,6057,6059,6067,6068,6078,6092,6099,


Stauffer, et al.       Expires September 27, 2014              [Page 15]


Internet-Draft            Supercharged Code                   March 2014


   6102,6107,6136,6151,6169,6189,6191,6218,6233,6249,6271,6274,6296,6318
   ,6352,6363,6376,6407,6430,6435,6441,6463,6486,6491,6502,6512,6518,652
   0,6534,6542,6549,6553,6589,6590,6593,6599,6614,6625,6634,6643,6655,66
   70,6680,6684,6691,6692,6701,6708,6711,6724,6730,6732,6752,6799,6803,6
   809,6812,6834,6849,6855,6877,6878,6879,6899,6907,6919,6936,6945,6946,
   6954,6955,6956,6958,6981,7000,7011,7030,7032,7033,7108,7111,7127,7164
   ,7171,7175,7179,7181,7185,7225,7226,7281,7288,7295,7307,7325,7359,736
   0,7390,7392,7411,7476,7520,7535,7548,7552,7558,7567,7589,7596,7616,76
   45,7675,7679,7714,7726,7747,7770,7780,7785,7805,7818,7855,7870,7883,7
   923,7935,7936,7953,7974,7999,8028,8030,8069,8074,8093,8104,8111,8122,
   8150,8154,8172,8173,8189,8192,8193,8194,8223,8236,8290,8304,8377,8425
   ,8438,8439,8464,8481,8492,8521,8556,8559,8575,8582,8595,8602,8606,862
   4,8628,8648,8654,8666,8672,8689,8738,8739,8744,8775,8787,8837,8841,88
   42,8860,8928,8929,8970,8977,8993,9009,9019,9020,9029,9041,9051,9087,9
   111,9151,9195,9208,9298,9303,9327,9344,9352,9360,9364,9388,9400,9402,
   9446,9448,9449,9461,9462,9470,9485,9497,9512,9539,9546,9560,9572,9601
   ,9612,9642,9649,9653,9677,9689,9692,9704,9708,9758,9765,9794,9813,986
   0,9916,9922,9927,9949,9971,9978,9981,9986,9987,10017,10040,10065,1007
   3,10084,10097,10105,10120,10124,10134,10166,10187,10197,10202,10204,1
   0241,10242,10279,10308,10324,10336,10351,10361,10458,10460,10567,1064
   3,10676,10705,10712,10717,10759,10786,10787,10857,10883,10899,10911,1
   0933,10944,10958,10963,11011,11015,11024,11036,11039,11049,11060,1111
   9,11130,11146,11172,11203,11210,11216,11219,11230,11245,11316,11358,1
   1371,11376,11423,11475,11534,11590,11649,11653,11677,11686,11707,1171
   1,11740,11748,11751,11780,11823,11829,11843,11890,11896,11919,11947,1
   1956,11976,12026,12037,12045,12072,12087,12108,12119,12154,12160,1220
   8,12215,12216,12228,12229,12235,12247,12294,12333,12400,12437,12455,1
   2458,12460,12469,12471,12510,12528,12567,12569,12593,12685,12694,1270
   4,12721,12726,12754,12790,12817,12857,12914,12928,12936,12956,13002,1
   3012,13026,13030,13035,13038,13057,13067,13082,13114,13143,13159,1319
   3,13204,13214,13270,13278,13284,13326,13335,13417,13421,13423,13460,1
   3479,13558,13607,13695,13696,13742,13764,13816,13827,13833,13837,1387
   4,13879,13974,13987,14022,14100,14115,14140,14202,14272,14342,14350,1
   4370,14376,14385,14393,14408,14409,14415,14417,14442,14486,14509,1456
   0,14565,14713,14729,14743,14755,14798,14862,14874,14913,14934,14990,1
   5007,15011,15120,15170,15194,15217,15227,15235,15285,15314,15321,1532
   5,15332,15438,15499,15573,15611,15651,15668,15732,15735,15741,15757,1
   5780,15808,15813,15847,15870,15941,15953,15977,16002,16017,16060,1610
   8,16161,16286,16287,16304,16336,16374,16377,16384,16414,16505,16563,1
   6623,16665,16670,16674,16689,16691,16710,16727,16743,16794,16828,1685
   1,16900,16974,17005,17024,17029,17038,17039,17051,17086,17098,17148,1
   7151,17195,17206,17266,17316,17323,17326,17331,17357,17376,17466,1748
   9,17531,17559,17642,17681,17791,17868,17926,17929,17988,17991,18009,1
   8026,18027,18056,18116,18168,18232,18307,18309,18438,18503,18504,1851
   1,18590,18628,18629,18630,18636,18647,18672,18691,18694,18719,18909,1
   8988,19023,19036,19096,19126,19132,19139,19193,19204,19210,19277,1930
   4,19314,19325,19539,19544,19547,19631,19632,19635,19675,19700,19705,1


Stauffer, et al.       Expires September 29, 2014              [Page 16]


Internet-Draft            Supercharged Code                   March 2014


   9740,19748,19921,19939,19951,19972,19985,20042,20052,20133,20141,2015
   2,20173,20230,20245,20269,20287,20335,20355,20396,20407,20455,20501,2
   0564,20580,20583,20664,20683,20710,20768,20776,20778,20789,20794,2098
   8,21058,21087,21141,21143,21151,21186,21199,21216,21224,21385,21412,2
   1468,21475,21478,21479,21486,21487,21515,21569,21616,21629,21673,2170
   2,21729,21737,21747,21852,21927,21969,22060,22062,22068,22073,22114,2
   2131,22244,22301,22320,22366,22433,22450,22482,22490,22498,22536,2272
   7,22787,22947,22994,23010,23026,23063,23084,23135,23158,23180,23252,2
   3392,23457,23491,23500,23568,23607,23721,23730,23787,23935,23971,2399
   1,24023,24185,24215,24232,24398,24406,24476,24548,24550,24555,24562,2
   4566,24591,24592,24616,24633,24673,24721,24735,24743,24761,24832,2489
   1,24967,24976,25062,25080,25230,25391,25407,25433,25463,25493,25543,2
   5613,25668,25756,25919,26022,26048,26050,26092,26291,26297,26329,2634
   2,26371,26535,26566,26582,26676,26741,26838,26908,26910,26973,26984,2
   7111,27119,27163,27256,27296,27353,27392,27428,27492,27594,27644,2766
   6,27682,27771,27885,27895,27959,27987,28088,28116,28134,28137,28248,2
   8263,28365,28466,28548,28549,28787,28816,28845,28966,29002,29042,2905
   4,29072,29127,29138,29265,29326,29345,29434,29481,29487,29500,29588,2
   9731,29816,29827,29868,29905,29964,30037,30097,30153,30169,30280,3034
   6,30405,30433,30461,30493,30513,30550,30583,30646,30654,30909,30915,3
   0921,30930,30974,30997,31052,31056,31142,31199,31283,31285,31303,3150
   5,31578,31605,31948,31957,31997,32124,32139,32142,32272,32403,32555,3
   2601,32630,32631,32648,32699,32768,32807,32849,32912,32932,32961,3296
   5,33129,33171,33200,33282,33334,33623,34258,34302,34654,34708,35024,3
   5031,35388,35395,35462,35488,35586,35600,35747,35750,35774,35802,3607
   1,36112,36189,36252,36254,36294,36328,36357,36448,36476,36477,36479,3
   6485,36637,36749,36849,36874,36894,37170,37185,37187,37227,37612,3769
   5,37701,37767,37793,37805,37815,37826,37906,37992,38008,38010,38046,3
   8080,38130,38236,38385,38763,38787,39166,39176,39201,39237,39288,3939
   8,39482,39643,39786,39831,39960,39980,40089,40105,40140,40152,40192,4
   0220,40274,40293,40303,40398,40549,40604,40625,40666,40690,40816,4084
   3,40847,40894,40896,40962,40969,41003,41087,41107,41132,41216,41226,4
   1265,41314,41321,41357,41367,41539,41576,41641,41717,41820,42033,4206
   7,42172,42490,42662,42795,42813,42916,43339,43351,43388,43482,43498,4
   3691,43840,43905,43924,43932,44033,44129,44279,44821,44883,44945,4495
   1,45097,45162,45359,45389,45557,45582,45638,45813,45830,45919,45960,4
   6038,46086,46104,46187,46281,46428,46463,46481,46574,47047,47324,4741
   8,47523,47717,48007,48264,48334,48489,48501,48702,48788,48976,48994,4
   9504,49550,49703,49711,49978,49995,50006,50338,50511,50799,50946,5094
   7,50951,50980,51017,51150,51244,51530,51616,51977,52007,52062,52364,5
   2441,52586,52598,52768,52883,52978,53047,53064,53114,53127,54024,5454
   6,54578,54735,54803,55123,55289,55510,55661,55744,55843,55885,55921,5
   6297,56403,56696,57113,57424,57614,57779,58294,58326,58721,58908,5934
   6,59541,59651,59882,60076,60164,60250,60618,60799,61144,61208,61217,6
   1617




Stauffer, et al.       Expires September 29, 2014              [Page 17]


Internet-Draft            Supercharged Code                   March 2014


2.7.8. Random Number Generator

   The SC code utilizes two random number generators.  The first uses
   the second.  The first is described by the following pseudo code:

   function b=RNG(a)

   for i = 0:7

       a = RNG_2( a, ( (a) % (89) ) )

       b = (b) % (a)

   end



   The second random number generator uses a selectable set of feedback
   taps.  The second is described by the following pseudo code:

   function a=RNG_2(a,b)

   tap_list=[32, 31, 30, 10

   32, 31, 29, 1

   32, 31, 26, 18

   32, 31, 26, 9

   32, 31, 26, 7

   32, 31, 23, 10

   32, 31, 22, 17

   32, 31, 21, 16

   32, 31, 21, 5

   32, 31, 18, 10

   32, 31, 16, 2

   32, 31, 15, 10

   32, 31, 14, 4


Stauffer, et al.       Expires September 29, 2014              [Page 18]


Internet-Draft            Supercharged Code                   March 2014


   32, 31, 13, 8

   32, 31, 9, 7

   32, 31, 5, 4

   32, 30, 29, 23

   32, 30, 29, 20

   32, 30, 29, 16

   32, 30, 29, 15

   32, 30, 27, 24

   32, 30, 27, 21

   32, 30, 27, 12

   32, 30, 27, 8

   32, 30, 26, 25

   32, 30, 26, 13

   32, 30, 25, 16

   32, 30, 23, 16

   32, 30, 23, 14

   32, 30, 23, 4

   32, 30, 21, 14

   32, 30, 19, 8

   32, 30, 19, 4

   32, 30, 17, 3

   32, 30, 15, 6

   32, 30, 11, 8

   32, 30, 11, 5


Stauffer, et al.       Expires September 29, 2014              [Page 19]


Internet-Draft            Supercharged Code                   March 2014


   32, 30, 8, 3

   32, 30, 7, 4

   32, 29, 28, 19

   32, 29, 27, 23

   32, 29, 27, 21

   32, 29, 27, 6

   32, 29, 26, 6

   32, 29, 25, 6

   32, 29, 22, 18

   32, 29, 19, 16

   32, 29, 17, 15

   32, 29, 15, 8

   32, 29, 6, 5

   32, 29, 6, 4

   32, 28, 25, 15

   32, 28, 25, 11

   32, 28, 25, 6

   32, 28, 23, 6

   32, 28, 15, 13

   32, 28, 9, 7

   32, 27, 26, 14

   32, 27, 25, 20

   32, 27, 25, 19

   32, 27, 25, 17


Stauffer, et al.       Expires September 29, 2014             [Page 20]


Internet-Draft            Supercharged Code                  March 2014


   32, 27, 25, 7

   32, 27, 25, 5

   32, 27, 23, 6

   32, 27, 21, 6

   32, 27, 20, 18

   32, 27, 18, 14

   32, 27, 15, 14

   32, 27, 14, 12

   32, 27, 14, 9

   32, 27, 8, 6

   32, 26, 25, 10

   32, 26, 23, 12

   32, 26, 22, 7

   32, 26, 20, 11

   32, 26, 19, 9

   32, 26, 19, 7

   32, 26, 18, 13

   32, 26, 15, 7

   32, 25, 24, 7

   32, 25, 22, 15

   32, 25, 17, 7

   32, 25, 14, 13

   32, 24, 22, 13

   32, 23, 21, 16


Stauffer, et al.       Expires September 29, 2014              [Page 21]


Internet-Draft            Supercharged Code                   March 2014


   32, 23, 18, 14

   32, 21, 20, 19

   32, 20, 17, 15

   32, 19, 18, 13]

   taps[0]=tap_list[b,0]

   taps[1]=tap_list[b,1]

   taps[2]=tap_list[b,2]

   taps[3]=tap_list[b,3]

   feedback=2.^^(32-taps[0]) + 2.^^(32-taps[1]) + 2.^^(32-taps[2]) +
   2.^^(32-taps[3])

   if( (a) & (1) )

       a = (a) ^ (feedback)

       a = (a) >> (1)

       a = (2^31) || (a)

   else

       a = (a) >> (1)

   end



2.7.9. Random Permutation

   The SC code utilizes a random permutation of length K to facilitate
   the construction of the random interleavers needed for the parallel
   filter codes.  The random permutation is given by the following
   pseduocode.  The RNG_2 function is defined in section 2.7.8.

   function [permutation,the_seed]= Generate_Permutation(a,b)

   for i=0:a-1

      permutation[i] = i + 1


Stauffer, et al.       Expires September 29, 2014             [Page 22]


Internet-Draft            Supercharged Code                  March 2014


   end



   for i=0:a-1

       c = RNG_2(b,1)

       b = ( (c) % (a-(i-1)) ) + i

       d = permutation[i]

       permutation[i] = permutation[b]

       permutation[b] = d

   end



2.7.10. RS Generator

   A Reed Solomon code is utilized in the construction of the SC code.
   Its construction is described by the following pseudo code.  The
   GF_exp and the GF_Multiply functions are defined in section 2.7.13.

   function G_V_RS = RS_gen(K,N)

   Gt=zeros[N,K]

   for i=0:N-1

       for k=0:K-1

           a = ((i+1)*k) % (2^^8-1)

           Gt[i,k]=GF_exp(a)

       end

   end



   G1=Gt[1:K,1:K]

   G2=Gt[K+1:N,1:K]


Stauffer, et al.       Expires September 29, 2014             [Page 23]


Internet-Draft            Supercharged Code                  March 2014


   G_V_RS = GF_Multiply(G2,G1^^-1)



   GF_Multiply implementes G2*G1_inv where the multiplication and
   addition are performend in the GF field.  The matrix inverse G1^^-1
   can be easily implemented using Gaussian Elimination for the small
   matrix G1.

2.7.11. RS Code

   If the number of transmit symbols N is optionally limited to N<=256
   and signaled using R=1, then the following pseudo code is used to
   generate matrix P.  The RS_gen function is defined in section 2.7.10.
   N is given by the FEC-OTI-Max-Number-of-Encoding-Symbols.


   Num_V_RS = N - K

   B_1 = RS_gen(K,K+Num_V_RS)

   P = [I[K]

        B_1 ]

   Num_B = 0

   K_eff = K



2.7.12. SC_Filter_Data

   [Filter_data, filter_N]=SC_filter_data(z)

   Filter_data=[0,2147483648,2863311531,3221225472,3435973837,3579139413
   ,3681400539,3758096384,3817748708,3865470566,3904515724,3937053355,39
   64585196,3988183918,4008636143,4026531840,4042322161,4056358002,40689
   16386,4080218931,4090445044,4099741510,4108229587,4116010325,41231686
   04,4129776246,4135894433,4141575607,4146864975,4151801719,4156419964,
   4160749568,4164816772,4168644728,4172253945,4175662649,4178887099,418
   1941841,4184839929,4187593114,4190211996,4192706170,4195084336,419735
   4403,4199523578,4201598442,4203585013,4205488811,4207314902,420906795
   0,4210752251,4212371771,4213930177,4215430865,4216876982,4218271451,4
   219616993,4220916136,4222171240,4223384508,4224557996,4225693630,4226
   793212,4227858432,4228890876,4229892034,4230863307,4231806012,4232721



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   393,4233610620,4234474799,4235314972,4236132128,4236927197,4237701065
   ,4238454568,4239188500,4239903613,4240600621,4241280205,4241943008,42
   42589646,4243220702,4243836733,4244438269,4245025816,4245599856,42461
   60849,4246709236,4247245437,4247769853,4248282869,4248784852,42492761
   55,4249757114,4250228053,4250689283,4251141099,4251583788,4294967295]

   filter_N=min(100,z)

   Filter_data[Filter_N-1]=4294967295


2.7.13. GF(256) Operations

   The SC code utilizes Galois field arithmetic in GF(256).  The
   primitive polynomial is D^^8 + D^^4 + D^^3 + D^^2 + 1.  The
   b=GF_exp(a) function raises the primitive element to the supplied
   power, a.  The function C=GF_Multiply(A,B) multiplies two matrices in
   the Galois field.

3. FEC Packets

   Encoded packets are constructed using a 4 byte FEC Payload ID
   followed by transmit symbols.  The Source ID field (SID) of the FEC
   Payload ID identifies the Source ID of the first transmit symbol in
   the packet.  Subsequent transmit symbols have sequential increasing
   SIDs.  If the last transmit symbol of a packet contains source
   padding, these padding bytes may be excluded from the packet.
   Otherwise, packets must contain only whole transmit symbols.

   It is RECOMMENDED that each packet include exactly one transmit
   symbol.  Multiple transmit symbols per packet SHALL also be
   supported.

3.1. Segmentation

   In order to encode large files within the working memory constraint,
   the source file may need to be segmented into transmit blocks and
   working blocks.

3.1.1. Transmit Blocks

   Given a source file of size F bytes and a transmit symbol size of T
   bytes, the file can be divided into K_total=ceil(F/T) transmit
   symbols.  A source transmit block is a collection of KL or KS of
   these transmit symbols.  KL and KS may be different if the total
   number of source transmit blocks does not evenly divide the number of
   transmit symbols required to represent the file.  The number of


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   source transmit blocks with KL transmit symbols and the number of
   source transmit blocks with KS transmit symbols are communicated to
   the decoder using parameter Z.  After encoding, a transmit block
   consists of a source transmit block and a repair transmit block.

   The transmit blocks are ordered such that the first ZL transmit block
   are encoded from source transmit blocks of size KL transmit symbols.
   The remaining ZS transmit blocks are encoded from source transmit
   blocks are of size KS transmit symbols.  Given Z, the first
   ZL=ceil(K_total/Z)*Z-K_total   transmit   blocks   are   of   size
   KL=floor(K_total/Z) and the remaining ZS=K_total-floor(K_total/Z)*Z
   transmit blocks are of size KS=ceil(K_total/Z).

3.1.2. Working Blocks

   In order to satisfy the working memory requirement, the transmit
   symbols can be further subdivided into working symbols.  The working
   symbols are ordered in a packet such that the first ceil(T/AL/Ns)*Ns-
   T/AL working-blocks are of size TWL=floor(T/AL/Ns) and the remaining
   T/AL-floor(T/AL/Ns)*Ns working-blocks are of size TWS=ceil(T/AL/Ns)
   in a given packet.  A working block is then a collection of working
   symbols.  The size of the working symbols are selected such that an
   entire source working block can fit into the working memory, where
   the source working block is the portion of the working block
   consisting of only source data and not repair data.  The ith working
   block consists of the ith working symbol of transmit symbols of a
   transmit block.  The KL (or KS) transmit symbols of a source transmit
   block  can  be  viewed  as  a  collection  of  working  symbols  or
   equivalently as a collection of source working blocks.

   After encoding, a working block consists of a source working block
   and a repair working block.  The receiver attempts to decode on a
   subset of the source and repair working symbols in a working block.

3.1.3. Padding

   In cases where effective number of transmit symbols used by the
   encoder and decoder, K_eff, is K_eff>K, then K_eff-K transmit symbols
   must be padded (with 0) to the data before encoding.  These padded
   symbols do not need to be transmitted, as the decoder is aware that
   they are padding.  (Padding SIDs 0 to K_eff-K-1 MAY be transmitted,
   but it is RECOMMENDED that they are not.)

4. Parameter Selection

   The code requires F, T, Z, Ns, and AL.    F is the total file size in
   Bytes.  T is the transmit symbol size in bytes, and it is RECOMMENDED


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   that it be equal to the packet payload size.  The number of transmit
   blocks Z MUST be chosen such that KL<=K_max, where KL is computed in
   section 3.1.1.   K_max is the maximum value in section 2.7.7.

   The number of working symbols, Ns, MUST be chosen small enough such
   that KL*TWL is less than or equal to the working memory requirement.
   The byte alignment, AL, is to be chosen based on the protocol and the
   typical machine architectures, a value of 4 (bytes) is RECOMMENDED.

5. Control Messages

   This section describes control messages that are used by the FEC.
   All fields are big-endian.

5.1. FEC Payload ID

   The FEC payload ID is a 4-byte field defined as follows:

   [0:7] TBN, (8 bits, unsigned integer): A non-negative integer
   identifier indicating the transmit block number.

   [8:31] SID , (24 bits, unsigned integer): A non-negative integer
   identifier indicating the transmit symbols in the packet.  SID 0 to
   K-1 indicate systematic symbols.

   The FEC Payload ID is shown in Figure 4.

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |      TBN      |                       SID                     |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
             Figure 4  FEC Payload ID format

5.2. FEC Object Transmission Information

5.2.1. FEC Encoding ID


   The value of the FEC Encoding ID MUST be 7, as assigned by IANA (see
   Section 8).


5.2.2. Common

   The Common FEC Object Transmission Information elements used by this
   FEC Scheme are:


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   [0:39] Transfer Length (F), (40 bits, unsigned integer): A non-
   negative integer.  This is the transfer length of the object in
   bytes.

   [40:47] are reserved.

   [48:63] Transmit Symbol Size (T), (16 bits, unsigned integer): A
   positive integer that is less than 2^^16.  This is the size of a
   transmit symbol in units of bytes.

   The encoded Common FEC Object Transmission Information format is
   shown in Figure 5.

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                      Transfer Length (F)                      |
   +               +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |               |    Reserved   |           Symbol Size (T)     |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
             Figure 5  Encoded Common FEC Object Transmission
             Information for Supercharged FEC Scheme

5.2.3. Scheme Specific

   The following parameters are carried in the Scheme-Specific FEC
   Object Transmission Information element for this FEC Scheme:

   [0:7] Z: The number of transmit blocks (8 bits, unsigned integer)

   [8:23] Ns: The number of working blocks (16 bits, unsigned integer)

   [24:30] AL: A symbol alignment parameter (7 bits, unsigned integer)

   [31] R: 0: Default 1: OPTIONALLY indicates that the maximum value of
   N satisfies N<=256 (1 bit, boolean)

   The encoded Specific FEC Object Transmission Information format is
   shown in Figure 5.

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |      Z        |              Ns               |     Al      |R|
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
             Figure 6  FEC Payload ID format



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6. Conventions used in this document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC-2119 [RFC2119].

   In this document, these words will appear with that interpretation
   only when in ALL CAPS. Lower case uses of these words are not to be
   interpreted as carrying RFC-2119 significance.

7. Security Considerations

   Users could potentially be subject to a denial of service attack if a
   single erroneous packet is injected into the delivery stream.
   Therefore, it is RECOMMENDED that source authentication and integrity
   checking are applied to the file or data object before delivering
   decoded data to applications.  The hashing methodology of SHA-256 is
   an example [2].

8. IANA Considerations

   Values of FEC Encoding IDs and FEC Instance IDs are subject to IANA
   registration.  For general guidelines on IANA considerations as they
   apply to this document, see [RFC5052].  IANA is requested to assign a
   value under the ietf:rmt:fec:encoding name-space to "Supercharged
   Code" as the FEC Encoding ID value associated with this
   specification, preferably the value 7.

9. References

9.1. Normative References

   [1]   Bradner, S., "Key words for use in RFCs to Indicate Requirement
         Levels", BCP 14, RFC 2119, March 1997.

   [2]   "Secure Hash Standard", National Institute of Standards
         and Technology FIPS PUB 180-3, October 2008.

9.2. Informative References

   [3]   Timothy Vismor, "Matrix Algorithms."

   [4]   Sergio Pissanetzky, "Sparse Matrix Technology," Academic Press,
         London (1984).



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   [5]   Timothy A. Davis, "Direct Methods for Sparse Linear Systems"
         SIAM, Philadelphia, Pa (2006)

   [6]   Yousef Saad, "Iterative Methods for Sparse Linear Systems" 2nd
         Ed. SIAM, Philadelphia, Pa (2003)

   [7]   I.S. Duff, A.M. Erisman, and J. K. Reid, "Direct Methods for
         Sparse Matrices" (2008) (ISBN: 978-0198534082)

   [8]   John K. Reid, "Solution of linear systems of equations: Direct
         methods" (1977)

   [9]   Golub, G.H. "Numerical methods for solving linear least-squares
         problems" Numerische  Mathematik Volumne 7, Number 3 (1965) pp
         206-216

10. Acknowledgments

   This document was prepared using 2-Word-v2.0.template.dot.

Authors' Addresses

   Erik Stauffer
   Broadcom
   190 Mathilda Place
   Sunnyvale, Ca 94086

   Email: eriks@broadcom.com


   BZ Shen
   Broadcom
   5300 California Avenue
   Irvine, CA 92617

   Email: bzshen@broadcom.com

   Soumen Chakraborty
   Broadcom
   RMZ Ecospace
   Bellandur
   Bangalore 560037, India

   Email: soumen@broadcom.com





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   Djordje Tujkovic
   Broadcom
   190 Mathilda Place
   Sunnyvale, Ca 94086

   Email: djordje@broadcom.com

   Jing Huang
   Broadcom
   190 Mathilda Place
   Sunnyvale, Ca 94086

   Email: jingh@broadcom.com

   Shiv Shet
   Broadcom
   RMZ Ecospace
   Bellandur
   Bangalore 560037, India

   Email: shivaprakash@broadcom.com


   Kamlesh Rath
   Broadcom
   190 Mathilda Place
   Sunnyvale, Ca 94086

   Email: krath@broadcom.com




















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