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NWCRG                                                           J. Heide
Internet-Draft                                             Steinwurf Aps
Intended status: Informational                                    S. Shi
Expires: August 15, 2019                                        K. Fouli
                                                               M. Medard
                                              Code On Network Coding LLC
                                                                V. Chook
                                                            Inmarsat PLC
                                                       February 11, 2019


     Random Linear Network Coding (RLNC): Background and Practical
                             Considerations
                  draft-heide-nwcrg-rlnc-background-00

Abstract

   This document describes the use of Random Linear Network Coding
   (RLNC) schemes for reliable data transport.  Both block and sliding
   window RLNC code implementations are described.  By providing erasure
   correction using randomly generated repair symbols, such RLNC-based
   schemes offer advantages in accommodating varying frame sizes and
   dynamically changing connections, reducing the need for feedback, and
   lowering the amount of state information needed at the sender and
   receiver.  The practical considerations' section identifies RLNC-
   encoded symbol representation as a valuable target for
   standardization.

Requirements Language

   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].

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."



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   This Internet-Draft will expire on August 15, 2019.

Copyright Notice

   Copyright (c) 2019 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
   (https://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   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.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Random Linear Network Coding (RLNC) Basics  . . . . . . .   3
     1.2.  Generation-Based RLNC . . . . . . . . . . . . . . . . . .   5
     1.3.  Sliding Window RLNC . . . . . . . . . . . . . . . . . . .   7
     1.4.  Recoding  . . . . . . . . . . . . . . . . . . . . . . . .   8
   2.  Practical Considerations  . . . . . . . . . . . . . . . . . .   9
     2.1.  Symbol Representation . . . . . . . . . . . . . . . . . .   9
       2.1.1.  Symbol Representation as a Standardization Approach .   9
       2.1.2.  Coding Parameter Design Considerations  . . . . . . .  12
   3.  Security Considerations . . . . . . . . . . . . . . . . . . .  13
   4.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  13
   5.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  13
     5.1.  Normative References  . . . . . . . . . . . . . . . . . .  13
     5.2.  Informative References  . . . . . . . . . . . . . . . . .  14
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  14

1.  Introduction

   Network Coding is a coding discipline that jointly improves network
   reliability and efficiency.  In general communication networks,
   source coding is performed as a compression mechanism to reduce data
   redundancy and to reduce resources necessary for data transportation
   over the network.  Channel coding, on the other hand, introduces
   redundancy for data transmission reliability over lossy channels.
   Network coding adds another layer of coding in-between these two.
   Random Linear Network Coding (RLNC) is an efficient network coding
   approach that enables network nodes to generate independently and
   randomly linear mappings of input to output data symbols over a
   finite field.



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   This document provides background on RLNC operation.  The document
   also includes an open section for practical considerations where
   topics such as standardization and RLNC-encoded symbol
   representations are addressed.

1.1.  Random Linear Network Coding (RLNC) Basics

   Unlike conventional communication systems based on the "store-and-
   forward" principle, RLNC allows network nodes to independently and
   randomly combine input source data into coded symbols over a finite
   field [HK03].  Such an approach enables receivers to decode and
   recover the original source data as long as enough linearly
   independent coded symbols, with sufficient degrees of freedom, are
   received.  At the sender, RLNC can introduce redundancy into data
   streams in a granular way.  At the receiver, RLNC enables progressive
   decoding and reduces feedback necessary for retransmission.
   Collectively, RLNC provides network utilization and throughput
   improvements, high degrees of robustness and decentralization,
   reduces transmission latency, and simplifies feedback and state
   management.

   To encode using RLNC, original source data are divided into symbols
   of a given size and linearly combined.  Each symbol is multiplied
   with a scalar coding coefficient drawn randomly from a finite field,
   and the resulting coded symbol is of the same size as the original
   data symbols.

   Thus, each RLNC encoding operation can be viewed as creating a linear
   equation in the data symbols, where the random scalar coding
   coefficients can be grouped and viewed as a coding vector.
   Similarly, the overall encoding process where multiple coded symbols
   are generated can be viewed as a system of linear equations with
   randomly generated coefficients.  Any number of coded symbols can be
   generated from a set of data symbols, similarly to expandable forward
   error correction codes specified in [RFC5445] and [RFC3453].  Coding
   vectors must be implicitly or explicitly transmitted from the sender
   to the receiver for successful decoding of the original data.  For
   example, sending a seed for generating pseudo-random coding
   coefficients can be considered as an implicit transmission of the
   coding vectors.  In addition, while coding vectors are often
   transmitted together with coded data in the same data packet, it is
   also possible to separate the transmission of coding coefficient
   vectors from the coded data, if desired.

   To reconstruct the original data from coded symbols, a network node
   collects a finite but sufficient number of degrees of freedom for
   solving the system of linear equations.  This is beneficial over
   conventional approaches as the network node is no longer required to



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   gather each individual data symbol.  In general, the network node
   needs to collect slightly more independent coded symbols than there
   are original data symbols, where the slight overhead arises because
   coding coefficients are drawn at random, with a non-zero probability
   that a coding vector is linearly dependent on another coding vector,
   and that one coded symbol is linearly dependent on another coded
   symbol.  This overhead can be made arbitrarily small, provided that
   the finite field used is sufficiently large.

   A unique advantage of RLNC is the ability to re-encode or "recode"
   without first decoding.  Recoding can be performed jointly on
   existing coded symbols, partially decoded symbols, or uncoded
   systematic data symbols.  This feature allows intermediate network
   nodes to re-encode and generate new linear combinations on the fly,
   thus increasing the likelihood of innovative transmissions to the
   receiver.  Recoded symbols and recoded coefficient vectors have the
   same size as before and are indistinguishable from the original coded
   symbols and coefficient vectors.

   In practical implementations of RLNC, the original source data are
   often divided into multiple coding blocks or "generations" where
   coding is performed over each individual generation to lower the
   computational complexity of the encoding and decoding operations.
   Alternatively, a convolutional approach can be used, where coding is
   applied to overlapping spans of data symbols, possibly of different
   spanning widths, viewed as a sliding coding window.  In generation-
   based RLNC, not all symbols within a single generation need to be
   present for coding to start.  Similarly, a sliding window can be
   variable-sized, with more data symbols added to the coding window as
   they arrive.  Thus, innovative coded symbols can be generated as data
   symbols arrive.  This "on-the-fly" coding technique reduces coding
   delays at transmit buffers, and together with rateless encoding
   operations, enables the sender to start emitting coded packets as
   soon as data is received from an upper layer in the protocol stack,
   adapting to fluctuating incoming traffic flows.  Injecting coded
   symbols based on a dynamic transmission window also breaks the
   decoding delay lower bound imposed by traditional block codes and is
   well suited for delay-sensitive applications and streaming protocols.

   When coded symbols are transmitted through a communication network,
   erasures may occur, depending on channel conditions and interactions
   with underlying transport protocols.  RLNC can efficiently repair
   such erasures, potentially improving protocol response to erasure
   events to ensure reliability and throughput over the communication
   network.  For example, in a point-to-point connection, RLNC can
   proactively compensate for packet erasures by generating Forward
   Erasure Correcting (FEC) redundancy, especially when a packet erasure
   probability can be estimated.  As any number of coded symbols may be



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   generated from a set of data symbols, RLNC is naturally suited for
   adapting to network conditions by adjusting redundancy dynamically to
   fit the level of erasures, and by updating coding parameters during a
   session.  Alternatively, packet erasures may be repaired reactively
   by using feedback requests from the receiver to the sender, or by a
   combination of FEC and retransmission.  RLNC simplifies state and
   feedback management and coordination as only a desired number of
   degrees of freedom needs to be communicated from the receiver to the
   sender, instead of indications of the exact packets to be
   retransmitted.  The need to exchange packet arrival state information
   is therefore greatly reduced in feedback operations.

   The advantages of RLNC in state and feedback management are apparent
   in a multicast setting.  In this one-to-many setup, uncorrelated
   losses may occur, and any retransmitted data symbol is likely to
   benefit only a single receiver.  By comparison, a transmitted RLNC
   coded symbol is likely to carry a new degree of freedom that may
   correct different errors at different receivers simultaneously.
   Similarly, RLNC offers advantages in coordinating multiple paths,
   multiple sources, mesh networking and cooperation, and peer-to-peer
   operations.

   A more detailed introduction to network coding including RLNC is
   provided in the books [MS11] and [HL08].

1.2.  Generation-Based RLNC

   This section describes a generation-based RLNC scheme.

   In generation-based RLNC, input data as received from an upper layer
   in the protocol stack is segmented into equal-sized blocks, denoted
   as generations, and each generation is further segmented into equal-
   sized data symbols for encoding, with paddings added when necessary.
   Encoding and decoding are performed over each individual generation.
   Figure 1 below provides an illustrative example where each generation
   includes four data symbols, and a systematic RLNC code is generated
   with rate 2/3.














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   Data Symbols:
             Generation-1                 Generation-2
    +============================++============================+
    | +---+  +---+  +---+  +---+ || +---+  +---+  +---+  +---+ |
    | | 1 |  | 2 |  | 3 |  | 4 | || | 5 |  | 6 |  | 7 |  | 8 | | ...
    | +---+  +---+  +---+  +---+ || +---+  +---+  +---+  +---+ |
    +============================++============================+
                     |                           |
                     |                           |
   Systematic        |                           |
   Symbols:          V                           V
    +---++---++---++---++---++---+ +---++---++---++---++---++---+
    | 1 || 2 || 3 || 4 || C1|| C2| | 5 || 6 || 7 || 8 || C3|| C4|  ...
    +---++---++---++---++---++---+ +---++---++---++---++---++---+

   Figure 1: Generation-based RLNC with rate 2/3, systematic encoding
   performed on data symbols within each generation.

   Symbols can be of any size, although symbol sizes typically depend on
   application or system specifications.  In scenarios with highly
   varying input data frame sizes, a small symbol size may be desirable
   for achieving flexibility and transmission efficiency, with one or
   more symbols concatenated to form a coded data packet.  In this
   context, existing basic FEC schemes [RFC5445] do not support the use
   of a single header for multiple coded symbols, whereas the symbol
   representation design as described in [Symbol-Representation]
   provides this option.

   For any protocol that utilizes generation-based RLNC, a setup process
   is necessary for establishing a connection and conveying coding
   parameters from the sender to the receiver.  Such coding parameters
   can include one or more of field size, code specifications, index of
   the current generation being encoded at the sender, generation size,
   code rate, and desired feedback frequency or probability.  Some
   coding parameters are updated dynamically during the transmission
   process, reflecting the coding operations over sequences of
   generations, and adjusting to channel conditions and resource
   availability.  For example, an outer header can be added to the
   symbol representation specified in [Symbol-Representation] to
   indicate the current generation encoded within the symbol
   representation.  Such information is essential for proper recoding
   and decoding operations, but the exact design of the outer header is
   outside the scope of the current document.  At the minimum, an outer
   header should indicate the current generation, generation size,
   symbol size, and field size.  Section 2 provides a detailed
   discussion of coding parameter considerations.





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1.3.  Sliding Window RLNC

   This section describes a sliding-window RLNC scheme.  Sliding window
   RLNC was first described in [SS09].

   In sliding-window RLNC, input data as received from an upper layer in
   the protocol stack is segmented into equal-sized data symbols for
   encoding.  In some implementations, the sliding encoding window can
   expand in size as new data packets arrive, until it is closed off by
   an explicit instruction, such as a feedback message that re-initiates
   the encoding window.  In some implementations, the size of the
   sliding encoding window is upper bounded by some parameter, fixed or
   dynamically determined by online behavior such as packet loss or
   congestion estimation.  Figure 3 below provides an example of a
   systematic finite sliding window code with rate 2/3.

    Data Symbols:
     +---+  +---+  +---+  +---+  +---+  +---+  +---+  +---+
     | 1 |  | 2 |  | 3 |  | 4 |  | 5 |  | 6 |  | 7 |  | 8 |      ...
     +---   +---+  +---+  +---+  +---+  +---+  +---+  +---+
     |    C1    |             |             |             |
     +==========+             |             |             |
     |            C2          |             |             |
     +========================+             |             |
                   |            C3          |             |
                   +========================+             |
                                 |              C4        |
                                 +========================+      ...
                            |
                            |
   Systematically           |
   Coded Symbols:           V
   +---++---++---++---++---++---++---++---++---++---++---++---+
   | 1 || 2 || C1|| 3 || 4 || C2|| 5 || 6 || C3|| 7 || 8 || C4|...
   +---++---++---++---++---++---++---++---++---++---++---++---+


   Figure 3: Finite sliding-window RLNC with code rate 2/3, systematic
   encoding performed on data symbols within the sliding coding window.

   For any protocol that utilizes sliding-window RLNC, a setup process
   is necessary for establishing a connection and conveying coding
   parameters from the sender to the receiver.  Such coding parameters
   can include one or more of field size, code specifications, symbol
   ordering, encoding window position, encoding window size, code rate,
   and desired feedback frequency or probability.  Some coding
   parameters can also be updated dynamically during the transmission
   process in accordance to channel conditions and resource



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   availability.  For example, an outer header can be added to the
   symbol representation specified in [Symbol-Representation] to
   indicate an encoding window position, as a starting index for current
   data symbols being encoded within the symbol representation.  Again,
   such information is essential for proper recoding and decoding
   operations, but the exact design of the outer header is outside the
   scope of the current document.  At the minimum, an outer header
   should indicate the current encoding window position, encoding window
   size, symbol size, and field size.  Section 2 provides a detailed
   discussion of coding parameter considerations.

   Once a connection is established, RLNC coded packets comprising one
   or more coded symbols are transmitted from the sender to the
   receiver.  The sender can transmit in either a systematic or coded
   fashion, with or without receiver feedback.  In progressive decoding
   of RLNC coded symbols, the notion of "seen" packets can be utilized
   to provide degree of freedom feedbacks.  Seen packets are those
   packet that have contributed to a received coded packet, where
   generally the oldest such packet that has yet to be declared seen is
   declared as seen [SS09].

1.4.  Recoding

   Recoding is the process where coded or partially decoded symbols are
   re-encoded without first being fully decoded.  To recode, both coded
   symbols and corresponding coding coefficient vectors are linearly
   combined, respectively, with new randomly generated recoding
   coefficients.  Recoded symbols and recoded coefficient vectors
   generally have the same size as before and are indistinguishable from
   the original coded symbols and coding coefficient vectors.  Recoding
   is typically performed at intermediate network nodes, in either an
   intra-session or an inter-session fashion.  Intra-session coding
   refers to coding between packets of the same flow or session, while
   inter-session coding refers to combination of packets from different
   flows or sessions in a network.

   As recoding requires the same operations on the coding coefficient
   vectors as applied to the coded symbols, coding coefficients must be
   updated by recoding coefficients.  This is generally achieved by
   having the coding coefficients accessible at recoding nodes so that
   they may be updated.  Thus, either the original coding coefficients
   or reversible representations of the coding coefficients need to be
   communicated from upstream nodes to the recoding nodes.








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2.  Practical Considerations

   This is an open section describing various practical considerations
   such as standardization approaches and implementation-related topics.

2.1.  Symbol Representation

   This sub-section argues for the specification of symbol
   representation as a starting point for network coding standardization
   and provides relevant coding parameter design considerations.

2.1.1.  Symbol Representation as a Standardization Approach

   Symbol representation specifies the format of the symbol-carrying
   data unit that is to be coded, recoded, and decoded.  In other words,
   symbol representation defines the format of the coding-layer data
   unit, including header format and symbol concatenation.

   Network Coding has fundamentally different requirements from
   conventional point-to-point codes.  Network coding owes its distinct
   requirements to its dynamic structure, leading to a highly
   reconfigurable symbol set.  For example:

   o  Coefficient Location: RLNC's encoding, recoding, and decoding
      process requires coefficients and payload to go through identical
      coding operations.  These operations are independent from the
      location of the coefficients.  As a consequence, coefficient
      location is flexible.  While some designs cluster coefficients
      together, other designs may distribute them throughout the payload
      in a manner that is specific to a given protocol.  [SS09]

   o  Number of coefficients: RLNC is designed to allow coding and
      recoding even when the number of input symbols is dynamic, leading
      to varying code density.  As a consequence, the number of
      coefficients and source data symbols need not be fixed.

   o  Payload Size: Although an identical size of symbols is desirable
      when performing coding operations, padding and fragmentation are
      viable not only at the source but also throughout the network, as
      illustrated in the example of Figure 5.  This allows flexibility
      in the payload size.

   o  Field: Although the finite field is typically a fixed system
      variable, this is not necessarily the case.  Network coding need
      not specify a single field for all payload components, as
      different symbols may belong to different fields (e.g., packet
      concatenation).  This feature does not necessarily complicate




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      coding, since finite field operations defined in a given field are
      typically valid in multiple other fields.

   Useful symbol representations should include provisions for the major
   coding functions that are relevant to the application, such as
   recoding, feedback, or inter-session network coding.  For example,
   recoding requires the coefficients to be accessible at the
   intermediate recoding nodes.  Hence, architectures and protocols
   requiring recoding must specify coefficient location.

   Furthermore, the example of Figure 4 illustrates how the knowledge of
   coefficient location affects the way a coded payload is fragmented,
   coded, and transported across the network.

   (a) Code-aware fragmentation
                                           +---+---------+
                                           | C |    D1   |
     +---+---------+---------+             +---+---------+
     | C |    D1   |    D2   |   +---->
     +---+---------+---------+             +---+---------+
                                           | C |    D2   |
                                           +---+---------+

   (b) Conventional fragmentation
                                           +-----------+
                                           |    D1     |
     +-----------+-----------+             +-----------+
     |    D1     |    D2     |   +---->
     +-----------+-----------+             +-----------+
                                           |    D2     |
                                           +-----------+


   Figure 4: Network operations such as fragmentation may be affected by
   symbol representation.  For example, whether coefficient location is
   (a) specified or (b) hidden may affect the way fragmentation is
   carried out.

   In Figure 4 (a), coefficient locations are known, allowing the
   association of the coefficient set C to both fragments D1 and D2 of
   original payload.  The ability to manipulate the original
   coefficients allows the newly formed packets to be recoded and
   decoded at the same coding layer.  Figure 4 (b) shows a case where
   the coding coefficient location are unknown.  This may occur when the
   file is pre-coded by a higher layer such as the application layer, or
   when coefficients are deliberately hidden for security reasons,
   leading to typical fragmentation without coefficient replication.




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   The absence of information on coefficient location has important
   implications.  One such implication is that any additional coding
   needs to be carried out within a new coding layer, potentially
   leading to higher computational and transport overheads.

   The elements discussed above demonstrate that the design choices
   related to symbol representation have a direct impact on the
   viability of protocols, topologies, and architecture.  The importance
   of symbol representation is illustrated in Figure 5, where the term
   "architecture" includes coding architecture (e.g., generation or
   sliding window), the layer placement of coding operations, and coding
   objectives (e.g., erasure correction, multisourcing, etc.).

                    +---------------+
                    |Architecture   |
                    |               |     Symbol
                    |               |     Representation
                    |               |
        +-------------------+       |          ^
        |Topology   |       |       |          |
        |           |  +-------------------+   |
        |           |  |----|       |      |   |
        |           |  |----| <----------------+
        |           |  |----|       |      |
        |           +---------------+      |
        |              |    |              |
        +-------------------+              |
                       |                   |
                       |           Protocol|
                       +-------------------+

   Figure 5: The specification of symbol representation has major
   implications on system architecture, topology, and protocol.

   Since symbol representation has implications on core design elements,
   it is expected that coding implementations that share protocol,
   architecture, and topology elements are likely to reuse the same
   symbol representation.  For example, implementations with security
   requirements can reuse a common symbol representation that hides
   coefficient locations.

   Another example can be found in [Symbol-Representation], which
   specifies symbol representation designs for generation-based and
   sliding window RLNC implementations.  These designs introduce highly
   reusable formats that concatenate multiple symbols and associate them
   with a single symbol representation header.





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2.1.2.  Coding Parameter Design Considerations

   For any protocol that utilizes generation-based or sliding-window
   RLNC, several coding parameters must be communicated from the sender
   to the receiver as part of the protocol design.  Without elaborating
   on all such parameters, this section examines those essential for
   symbol representation design, including field size, symbol size,
   maximum number of symbols, and maximum generation or window size.

   As RLNC is performed over a finite field, field size determines the
   complexity of the required mathematical computations.  Larger field
   sizes translate to higher probability of successful decoding, as
   randomly generated coding coefficient vectors are more likely to be
   independent from each other.  However, larger field sizes may also
   result in higher computational complexity, leading to longer decoding
   latency, higher energy usage, and other hardware requirements for
   both the encoder and the decoder.  A finite field size of 2 or the
   binary Finite Field FF(2) should always be supported since addition,
   multiplication, and division over FF(2) are equivalent to elementary
   XOR, AND, and IDENTITY operations respectively.  It is also desirable
   to support a field size of 2^8, corresponding to a single byte, and
   where operations are performed over the binary extension field
   FF(2^8) with polynomial x^8+x^4+x^3+x^2+1.

   The choice of symbol size typically depends on the application or
   system specification.  For example, a symbol size may be chosen based
   on the size of a maximum transmission unit (MTU) so that datagrams
   are not fragmented as they traverse a network, while also ensuring no
   symbol bits are unnecessarily wasted.  A symbol representation design
   can be flexible and accommodate any symbol size in bytes.  For
   example, an IP packet is typically in the range between 500 and 1500
   bytes, while a much smaller datagram having a size of 90 bytes may be
   used by satellite communication networks.  The symbol representation
   in [Symbol-Representation] can be configured to support either or
   both cases in different implementations.

   The generation size or coding window size is a tradeoff between the
   strength of the code and the computational complexity of performing
   the coding operations.  With a larger generation/window size, fewer
   generations or coding windows are needed to enclose a data message of
   a given size, thus reducing protocol overhead for coordinating
   individual generations or coding windows.  In addition, a larger
   generation/window size increases the likelihood that a received coded
   symbol is innovative with respect to previously received symbols,
   thus amortizing retransmission or FEC overheads.  Conversely, when
   coding coefficients are attached, larger generation/window sizes also
   lead to larger overheads per packet.  The generation/window size to




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   be used can be signaled between the sender and receiver when the
   connection is first established.

   Lastly, to successfully decode RLNC coded symbols, sufficient degrees
   of freedom are required at the decoder.  The maximum number of
   redundant symbols that can be transmitted is therefore limited by the
   number of linearly independent coding coefficient vectors that can be
   supported by the system.  For example, if coding vectors are
   constructed using a pseudo-random generator, the maximum number of
   redundant symbols that can be transmitted is limited by the number of
   available generator states.[RFC5445]

3.  Security Considerations

   This document does not present new security considerations.

4.  IANA Considerations

   This document has no actions for IANA.

5.  References

5.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC3453]  Luby, M., Vicisano, L., Gemmell, J., Rizzo, L., Handley,
              M., and J. Crowcroft, "The Use of Forward Error Correction
              (FEC) in Reliable Multicast", RFC 3453,
              DOI 10.17487/RFC3453, December 2002,
              <https://www.rfc-editor.org/info/rfc3453>.

   [RFC5445]  Watson, M., "Basic Forward Error Correction (FEC)
              Schemes", RFC 5445, DOI 10.17487/RFC5445, March 2009,
              <https://www.rfc-editor.org/info/rfc5445>.

   [Symbol-Representation]
              Heide, J., Shi, S., Fouli, K., Medard, M., and V. Chook,
              "Random Linear Network Coding (RLNC)-Based Symbol
              Representation", February 2018,
              <https://www.ietf.org/archive/id/
              draft-heide-nwcrg-rlnc-00.txt>.






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5.2.  Informative References

   [HK03]     Ho, T., Koetter, R., Medard, M., Karger, D., and M.
              Effros, "The Benefits of Coding over Routing in a
              Randomized Setting", July 2003,
              <http://ieeexplore.ieee.org/document/1228459/>.

   [HL08]     Ho, T. and D. Lun, "Network Coding: An Introduction",
              April 2008.

   [MS11]     Medard, M. and A. Sprintson, "Network Coding: Fundamentals
              and Applications", October 2011.

   [SS09]     Sundararajan, J., Shah, D., Medard, M., Mitzenmacher, M.,
              and J. Barros, "Network Coding Meets TCP", April 2009,
              <http://ieeexplore.ieee.org/document/5061931/>.

Authors' Addresses

   Janus Heide
   Steinwurf Aps
   Aalborg
   Denmark

   Email: janus@steinwurf.com


   Shirley Shi
   Code On Network Coding LLC
   Cambridge
   USA

   Email: xshi@alum.mit.edu


   Kerim Fouli
   Code On Network Coding LLC
   Cambridge
   USA

   Email: fouli@codeontechnologies.com










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   Muriel Medard
   Code On Network Coding LLC
   Cambridge
   USA

   Email: muriel.medard@codeontechnologies.com


   Vince Chook
   Inmarsat PLC
   London
   United Kingdom

   Email: Vince.Chook@inmarsat.com





































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