Internet Engineering Task Force                                  S. Yang
Internet-Draft                                                  CUHK(SZ)
Intended status: Informational                                  X. Huang
Expires: August 25, 2021                                      R.W. Yeung
                                                                    CUHK
                                                                J.K. Zao
                                                                    NCTU
                                                       February 21, 2021


            BATS Coding Scheme for Multi-hop Data Transport
                        draft-irtf-nwcrg-bats-00

Abstract

   BATS code is a class of efficient linear network coding scheme with a
   matrix generalization of fountain codes as the outer code, and batch-
   based linear network coding as the inner code.  This document
   describes a baseline BATS coding scheme for communication through
   multi-hop networks, and discusses the related research issues towards
   a more sophisticated BATS coding scheme.

Status of This Memo

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   This Internet-Draft will expire on August 25, 2021.

Copyright Notice

   Copyright (c) 2021 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



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   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.  Requirements Language . . . . . . . . . . . . . . . . . .   3
   2.  Procedures  . . . . . . . . . . . . . . . . . . . . . . . . .   4
     2.1.  Introduction  . . . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Data Delivery Procedures  . . . . . . . . . . . . . . . .   5
       2.2.1.  Source Node Data Partitioning and Padding . . . . . .   5
       2.2.2.  Source Node Outer Code Encoding Procedure . . . . . .   6
       2.2.3.  Recoding Procedures . . . . . . . . . . . . . . . . .   7
       2.2.4.  Destination Node Procedures . . . . . . . . . . . . .   8
     2.3.  Recommendation for the Parameters . . . . . . . . . . . .   8
     2.4.  Example DDP Packet Format . . . . . . . . . . . . . . . .   9
       2.4.1.  Packet Header . . . . . . . . . . . . . . . . . . . .   9
       2.4.2.  Packet Payload  . . . . . . . . . . . . . . . . . . .  10
       2.4.3.  Packet Footer . . . . . . . . . . . . . . . . . . . .  10
   3.  BATS Code Specification . . . . . . . . . . . . . . . . . . .  11
     3.1.  Common Parts  . . . . . . . . . . . . . . . . . . . . . .  11
     3.2.  Outer Code Encoder  . . . . . . . . . . . . . . . . . . .  12
     3.3.  Inner Code Encoder (Recoder)  . . . . . . . . . . . . . .  13
     3.4.  Belief Propagation Decoder  . . . . . . . . . . . . . . .  13
   4.  Research Issues . . . . . . . . . . . . . . . . . . . . . . .  14
     4.1.  Coding Design Issues  . . . . . . . . . . . . . . . . . .  14
     4.2.  Protocol Design Issues  . . . . . . . . . . . . . . . . .  15
     4.3.  Application Related Issues  . . . . . . . . . . . . . . .  16
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  17
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  17
     6.1.  Provision of Confidentiality Protection . . . . . . . . .  17
     6.2.  Countermeasures against Pollution Attacks . . . . . . . .  18
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  18
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  18
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  19
   Appendix A.  Additional Stuff . . . . . . . . . . . . . . . . . .  20
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  20

1.  Introduction

   This document specifies a baseline BATS code [Yang14] scheme for data
   delivery in multi-hop networks, and discusses the related research
   issues towards a more sophisticated scheme.  The BATS code described
   here includes an outer code and an inner code.  The outer code is a
   matrix generalization of fountain codes (see also the RapterQ code



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   described in RFC 6330 [RFC6330]), which inherits the advantages of
   reliability and efficiency and possesses the extra desirable property
   of being network coding compatible.  The inner code, also called
   recoding, is formed by linear network coding for combating packet
   loss, improving the multicast efficiency, etc.  A detailed design and
   analysis of BATS codes are provided in the BATS monograph [Yang17].

   A BATS coding scheme can be applied in multi-hop networks formed by
   wireless communication links, which are inherently unreliable due to
   interference.  Existing transport protocols like TCP use end-to-end
   retransmission, while network protocols such as IP might enable
   store-and-forward at the relays, so that packet loss would accumulate
   along the way.

   A BATS coding scheme can be used for various data delivery
   applications like file transmission, video streaming over wireless
   multi-hop networks, etc.  Different from traditional forward error
   correcting (FEC) schemes that are applied either hop-by-hop or end-
   to-end, the BATS coding scheme combines the end-to-end coding (the
   outer code) with certain hop-by-hop coding (the inner code), and
   hence can potentially achieve better performance.

   The baseline coding scheme described here considers a network with
   multiple communication flows.  For each flow, the source node encodes
   the data for transmission separately.  Inside the network, however,
   it is possible to mix the packets from different flows for recoding.
   In this document, we describe a simple case where recoding is
   performed within each flow.  Note that the same encoding/decoding
   scheme described here can be used with different recoding schemes as
   long as they follow the principle as we illustrate in this document.

   The purpose of the baseline BATS coding scheme is twofold.  First, it
   provides researchers and engineers a starting point for developing
   network communication applications/protocols based on BATS codes.
   Second, it helps to make the research issues more clear towards a
   sophisticated BATS code based network protocol.  Important research
   directions include the security issues, congestion control and
   routing algorithms for BATS codes, etc.

1.1.  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].







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2.  Procedures

2.1.  Introduction

   A BATS coding scheme includes an outer code encoder (also called
   encoder), an inner code encoder (also called recoder) and a decoder.
   The BATS coding scheme can be used for a single data flow that
   includes a single source and one or multiple destinations.  Thus
   there exists only one encoder with multiple recoders and decoders.
   The BATS coding scheme described in this document can be used by a
   Data Delivery Protocol (DDP) with the following procedures.

      Outer Code Encoding at a source node which has the data for
      transmission:

      *  The DDP provides the data to be delivered and the related
         information to the BATS encoder.

      *  The BATS encoder generates a sequence of batches, each
         consisting of a set of coded packets and the information
         pertaining to the batch.

      The batches generated at the source node are further recoded
      before transmitting:

      *  A BATS recoder generates recoded packets of a batch.

      *  The DDP forms and transmits the DDP packets using the batches
         and the corresponding batch information.

      Recoding at an intermediate node that does not need the data:

      *  The DDP extracts the batches and the corresponding batch
         information from its received DDP packets.

      *  A BATS recoder generates recoded packets of a batch.

      *  The DDP forms and transmits DDP packets using the recoded
         packets and the corresponding batch information.

      Decoding at a destination node that needs the data:

      *  The DDP extracts the batches and the corresponding batch
         information from its received DDP packets.

      *  A BATS decoder tries to recover the transmitted data using the
         received batches.




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      *  The DDP sends the decoded data to the application that needs
         the data.

2.2.  Data Delivery Procedures

   Suppose that the DDP has F octets of data for transmission.  We
   describe the procedures of one BATS session for transmitting the F
   octets.  There is a limit on F of a single BATS session.  If the
   total data has more than the limit, the data needs to be transmitted
   using multiple BATS sessions.  The limit on F of a single BATS
   session depends on the MTU (maximum transmission unit) of the
   network, which MUST be known by the DDP.  We have F is no more than
   (MTU-10)2^16-1 octets.

2.2.1.  Source Node Data Partitioning and Padding

   The DDP first determines the following parameters:

   o  Batch size (M): the number of coded packets in a batch.

   o  Recoding field size (q): the number of elements in the finite
      field for recoding. q is 2 or 2^8

   o  BATS payload size (TO): the number of payload octets in a BATS
      packet, including the coded data and the coefficient vector.

   Based on the above parameters, the parameters T, O and K are
   calculated as follows:

   o  O: the number of octets of a coefficient vector, calculated as O =
      ceil(M*log2(q)/8).

   o  T: the number of data octets of a BATS packet, calculated as T =
      TO - O.

   o  K: number of source packets, calculated as K = floor(F/T)+1.

   The data MUST be padded to have T*K octets, which will be partitioned
   into K source packets b[0], ..., b[K-1], each of T octets.  In our
   padding scheme, b[0], ..., b[K-2] are filled with data bits, and
   b[K-1] is filled with the remaining data octets and padding octets.
   Let P = K*T-F denote the number of padding octets.  We use b[K-1, 0],
   ..., b[K-1, T-P-1] to denote the T-P source octets and b[K-1, T-P],
   ..., b[K-1, T-1] to denote the P padding octets in b[K-1],
   respectively.  The padding process is shown in Figure 1.






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         Z = T - P
         Let bl be the last source packet b[K-1]
         for i = 1, 2, ... do
           if Z + i >= T - 1 do
               bl[Z...T-1] = i
               break
           bl[Z...Z+i-1] = i
           Z = Z + i

                      Figure 1: Data Padding Process

2.2.2.  Source Node Outer Code Encoding Procedure

   The DDP provides the BATS encoder with the following information:

   o  Batch size (M): the number of coded packets in a batch.

   o  Recoding field size (q): the number of elements in the finite
      field for recoding.

   o  MAX_DEG: the size of DD.

   o  The degree distribution (DD), which is an unsigned integer array
      of size MAX_DEG+1.

   o  A sequence of batch IDs (j, j = 0, 1, ...).

   o  Number of source packets (K).

   o  Packet size (T): the number of octets in a source packet.

   o  The source packets (b[i], i = 0, 1, ..., K-1).

   Using this information, the (outer code) encoder generates a batch
   for each batch ID.  For the batch ID j, the encoder returns the DDP
   that contains

   o  a sparse degree d[j], and

   o  M coded packets (x[j,i], i =0, 1, ..., M-1), each containing TO
      octets.

   The DDP will use the batches to form DDP packets to be transmitted to
   other network nodes towards the destination nodes.  The DDP MUST
   deliver with each coded packet its

   o  d: sparse degree




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   o  BID: batch ID

   The DDP MUST deliver the following information to each recoder:

   o  M: batch size M

   o  q: recoding field size

   The DDP MUST deliver the following information to each decoder:

   o  M: batch size

   o  q: recoding field size

   o  K: the number of source packets

   o  T: the number of octets in a source packet

   The BID is used by both recoders and decoders.  The BATS payload size
   TO MUST be known by all the nodes.

   The DDP will also include some necessary extra information in the
   packet header so that the network nodes can identify different BATS
   sessions, and different end-to-end communication flows.  However,
   such specifications are beyond the scope of this document.

2.2.3.  Recoding Procedures

   Both the source node and the intermediate nodes perform recoding on
   the batches before transmission.  At the source node, the recoder
   receives the batches from the outer code encoding procedure.  At an
   intermediate node, the DDP receives the DDP packets from the other
   network nodes, and should be able to extract coded packets and the
   corresponding batch information from these packets.

   The DDP provides the recoder with the following information:

   o  the batch size M,

   o  the recoding field size q,

   o  a number of received coded packets of the same batch, each
      containing TO octets, and

   o  link statistics, e.g., packet loss rates.

   For a received batch, the recoder determines a positive integer Mr,
   the number of recoded packets to be transmitted for the batch.  The



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   recoder uses the information provided by the DDP to generate Mr
   recoded packets, each containing TO octets.  The DDP uses the Mr
   recoded packets to form the DDP packets for transmitting.

2.2.4.  Destination Node Procedures

   A destination node needs the data transmitted by the source node.  At
   the destination node, the DDP receives DDP packets from the other
   network nodes, and should be able to extract coded packets and the
   corresponding batch information from these packets.

   The DDP provides the decoder with the following information:

   o  M: batch size,

   o  q: recoding field size,

   o  K: the number of source packets

   o  T: the number of octets of a source packet

   o  A sequence of batches, each of which is formed by a number of
      coded packets belonging to the same batch, with their
      corresponding batch IDs and degrees.

   The decoder uses this information to decode the K source packets.  If
   successful, the decoder returns the recovered K source packets to the
   DDP, which will use the K source packets to form the F octets data.
   The recommended padding process is shown as follows:

       // this procedure returns the number P of padding octets
       // at the end of b[K-1]
       Let bl be the last decoded source packet b[K-1]
       PL = bl[T-1]
       if PL == 1 do
           return P = 1
       WI = T - 1
       while bl[WI] == PL do
           WI = WI - 1
       return P = (1 + bl[WI]) * bl[WI] + T - WI - 1

                     Figure 2: Data Depadding Process

2.3.  Recommendation for the Parameters

   The recommendation for the parameters M and q is shown as follows:

   o  When q=2, M=16,32,64



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   o  When q=256, M=8,16,32,64

   It is RECOMMENDED that K is at least 128.  However, the encoder/
   decoder SHALL support an arbitrary positive integer value less than
   2^16.

2.4.  Example DDP Packet Format

   A DDP can form a DDP packet with a header (5 octets), a footer (3
   octets) and a payload (TO octets).  A DDP packet has totally 8+TO
   octets.

2.4.1.  Packet Header

   The BATS packet header has 40 bits (5 octets) and includes fields
   Packet_Count, Mq, Batch_ID, and Degree.

       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
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
       |           Packet_Count        |  Mq   |       Batch_ID        |
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
       |     Degree    |
       +-+-+-+-+-+-+-+-+

                   Figure 3: BATS packet header format.

   o  Packet_Count: 16-bit unsigned integer, specifying the number K of
      packets of the BATS session.

   o  Mq: 4-bit unsigned integer to specify the value of M and q as
      Table 1.

   o  Batch_ID: 12-bit unsigned integer, specifying the batch ID BID of
      the batch the packet belonging to.

   o  Degree: 8-bit unsigned integer, specifying the batch degree d of
      the batch the packet belonging to.













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                         +------+----+-----+----+
                         | Mq   | M  | q   | O  |
                         +------+----+-----+----+
                         | 0010 | 16 | 2   | 2  |
                         | 0100 | 32 | 2   | 4  |
                         | 0110 | 64 | 2   | 8  |
                         | 0001 | 8  | 256 | 8  |
                         | 0011 | 16 | 256 | 16 |
                         | 0101 | 32 | 256 | 32 |
                         | 0111 | 64 | 256 | 64 |
                         +------+----+-----+----+

                        Table 1: Values of Mq field

2.4.2.  Packet Payload

                     O                         T
         +-----------------------+-------------------------------+
         |   coefficient vector  |          coded data           |
         +-----------------------+-------------------------------+

                   Figure 4: BATS packet payload format.

   The payload has TO octets, where the first O octets contain the
   coefficient vector and the remaining T octets contain the coded data.
   Information in both fields MAY be encoded in JSON (ASCII) or protobuf
   (binary) formats.

   o  coefficient vector: O octets.  The range of the value of O is in
      Table 1.

   o  coded data: T octets.  T is at most MTU - 10, where 10 is the
      total of the header and footer length plus the minimum value of O.

2.4.3.  Packet Footer

         0                   1                   2
         0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
         +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
         |            signature          |  parity check |
         +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                   Figure 5: BATS packet footer format.

   The footer has three octets.

   o  signature: 2 octets.  A signature of the individual packet to
      prevent pollution attack.



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   o  parity check: 1 octet.  A parity check field used to verity the
      correctness of the packet.

3.  BATS Code Specification

3.1.  Common Parts

   The T octets of a source packets are treated as a column vector of T
   elements in GF(256).  Linear algebra and matrix operations over
   finite fields are assumed in this section.

   Suppose that a pseudorandom number generator Rand() which generates
   an unsigned integer of 32 bits is shared by both encoding and
   decoding.  The pseudorandom generator can be initialized by
   Rand_Init(S) with seed S.  When S is not provided, the pseudorandom
   generator is initialized arbitrarily.  One example of such a
   pseudorandom generator is defined in RFC 8682 [RFC8682].

   A function called BatchSampler is used in both encoding and decoding.
   The function takes two integers j and d as input, and generates an
   array idx of d integers and a d x M matrix G.  The function first
   initializes the pseudorandom generator with j, sample d distinct
   integers from 0 to K-1 as idx, and sample d*M integers from 0 to 255
   as G.  See the pseudocode in Figure 6.

   function BatchSampler(j,d)
       // initialize the pseudorandom generator by seed j.
       Rand_Init(j)
       // sample d distinct integers between 0 and K-1.
       for k = 0, ..., d-1 do
           r = Rand() % K
           while r already exists in idx do
               r = Rand() % K
           idx[k] = r

       // sample d x M matrix
       for r = 0, ..., d-1 do
           for c = 0,...,M-1 do
               G[r,c] = Rand() % 256

       return idx, G

                     Figure 6: Batch Sampler Function








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3.2.  Outer Code Encoder

   Define a function called DegreeSampler that return an integer d using
   the degree distribution DD.  We expect that the empirical
   distribution of the returning d converges to DD(d) when d < K.  One
   design of DegreeSampler is illustrated in Figure 7.

   function DegreeSampler(j, DD)
       Let CDF be an array
       CDF[0] = 0
       for i = 1, ..., MAX_DEG do
           CDF[i] = CDF[i-1] + DD[i]
       Rand_Init()
       r = Rand() % CDF[MAX_DEG]
       for d = 1, ..., MAX_DEG do
           if r >= CDF[d] do
               return min(d,K)
       return min(MAX_DEG,K)

                     Figure 7: Degree Sampler Function

   Let b[0], b[1], ..., b[K-1] be the K source packets.  A batch with
   BID j is generated using the following steps.

   o  Obtain a degree d by calling DegreeSampler with input j.

   o  Obtain idx and G[j] by calling BatchSampler with input j and d.

   o  Let B[j] = (b[idx[0]], b[idx[1]], ..., b[idx[d-1]]).  Form the
      batch X[j] = B[j]*G[j], whose dimension is T x M.

   o  Form the TO x M matrix Xr[j], where the first O rows of Xr[j] form
      the M x M identity matrix I with entries in GF(q), and the last T
      rows of Xr[j] is X[j].

   See the pseudocode of the batch generating process in Figure 8.

   function GenBatch(j)
       d = DegreeSampler(j)
       (idx, G) = BatchSampler(j,d)
       B = (b[idx[0]], b[idx[i]], ..., b[idx[d-1]])
       X = B * G
       Xr = [I_M; X]
       return Xr

                    Figure 8: Batch Generation Function





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3.3.  Inner Code Encoder (Recoder)

   The inner code comprises (random) linear network coding applied on
   the coded packets belonging to the same batch.  At a particular
   network node, recoded packets are generated by (random) linear
   combinations of the received coded packets of a batch.  The recoded
   packets have the same BID, sparse degree and coded packet length.

   The number Mr of recoded packets for a batch is decided first by the
   recoder.  Mr can be set as M.  When the link statistics is known, the
   recoder can try to obtain the link packet loss rate e for the link to
   transmit the recoded batch, and set Mr to be (1+e)M.

   Suppose that coded packets xr[i], i = 0, 1, ..., r-1, which have the
   same BID j, have been received at an intermediate node.  Using the
   recommended packet format, it can be verified whether the
   corresponding packet headers of these coded packets are the same.
   Then a recoded packet can be generated by one of the following two
   approaches:

   o  forwarding: when receiving xr[i], directly use xr[i] as a recoded
      packet.

   o  linear combination recoding: (randomly) choose a sequence of
      coefficients c[i], i = 0, 1, ..., r-1 from GF(q).  Generate
      c[0]xr[0]+c[1]xr[1]+...+c[r-1]xr[r-1] as a recoded packet.

   A recoder can combine these two approaches to generate recoded
   packets.  For example, the recoder will output xr[i], i = 0, 1, ...,
   r-1 as r systematic recoded packets and generate Mr-r recoded packets
   using linear combinations of randomly chosen coefficients.

3.4.  Belief Propagation Decoder

   The decoder receives a sequence of batches Yr[j], j = 0, 1, ..., n-1,
   each of which is a TO-row matrix over GF(256).  The degree d[j] of
   batch j is also known.  Let Y[j] be the submatrix of the last T rows
   of Yr[j].  When q = 256, let H[j] be the first M rows of Yr[j]; when
   q = 2, let H[j] be the matrix over GF(256) formed by embedding each
   bit in the first M/8 rows of Yr[j] into GF(256).

   By calling BatchSampler with input j and d[j], we obtain idx[j] and
   G[j].  According to the encoding and recoding processes described in
   Section 3.2 and Section 3.3, we have the system of linear equations
   Y[j] = B[j]G[j]H[j] for each received batch with ID j, where B[j] =
   (b[idx[j,0]], b[idx[j,1]], ..., b[idx[j,d-1]]) is unknown.





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   We describe a belief propagation (BP) decoder that can efficiently
   solve the source packets when a sufficient number of batches have
   been received.  A batch j is said to be decodable if rank(G[j]H[j]) =
   d[j] (i.e., the system of linear equations Y[j] = B[j]G[j]H[j] with
   B[j] as the variable matrix has a unique solution).  The BP decoding
   algorithm has multiple iterations.  Each iteration is formed by the
   following steps:

   o  Decoding step: Find a batches j that is decodable.  Solve the
      corresponding system of linear equations Y[j] = B[j]G[j]H[j] and
      decode B[j].

   o  Substitution step: Substitute the decoded source packets into
      undecodable batches.  Suppose that a decoded source packet b[k] is
      used in generating a undecodable Y[j].  The substitution involves
      1) removing the entry in idx[j] corresponding to k, 2) removing
      the row in G[j] corresponding to b[k], and 3) reducing d[j] by 1.

   The BP decoder repeats the above steps until no batches are decodable
   during the decoding step.

4.  Research Issues

   The baseline BATS coding scheme described in Section 2 and Section 3
   needs various refinement and complement towards a more sophisticated
   network communication application.  Various related research issues
   are discussed in this section, but the security related issues are
   left to Section 6.

4.1.  Coding Design Issues

   The BATS code specification in Section 3 has nearly optimal
   throughput when the number of source packets K is sufficiently large.
   But when K is small, the degree sampler function in Figure 7 and the
   BatchSampler function in Figure 6 based on a pseudorandom generator
   may not sample all the source packets evenly, so that some of the
   source packets are not well protected.  One approach to solve this
   issue is to generate a deterministic degree sequence when the number
   of batches is relatively small, and design a special pseudorandom
   generator that has a good sampling performance when K is small.

   The belief propagation decoder in Section 3.4 guarantees the recovery
   of a given fraction of the source packets.  To recover all the source
   packets, a precode can be applied to the source packets to generate a
   fraction of redundant packets before applying the outer code
   encoding.  Moreover, when the belief propagation decoder stops, it is
   possible to continue with inactivation decoding, where certain source
   packets are treated inactive so that a similar belief propagation



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   process can be resumed.  The reader is referred to RFC 6330 [RFC6330]
   for the design of a precode with a good inactivation decoding
   performance.

   There are research issues related to recoding discussed in
   Section 3.3.  One question is how many recoded packets to generate
   for each batch.  Though it is asymptotically optimal when using the
   same number of recoded packets for all batches, it has been shown
   that transmitting a different number of recoded packets for different
   batches can improve the recoding efficiency.  The intuition is that
   for a batch with a lower rank, a smaller number of recoded packets
   need to be transmitted.  This kind of recoding scheme is called
   adaptive recoding [Yin19].

   Packet loss in network communication is usually bursty, which may
   harm the recoding performance.  One way to resolve this issue is to
   transmit the packets of different batches in a mixed order, which is
   also called batch interleaving [Yin20].  How to efficiently
   interleave batches without increasing too much end-to-end latency is
   a research issue.

   Though we only focus on the BATS coding scheme with one source node
   and one destination node, a BATS coding scheme can be used for
   multiple source and destination nodes.  To benefit from multiple
   source nodes, we would need different source nodes to generate
   statistically independent batches.  For communicating the same data
   to multiple destination nodes, which is also call multicast, it is
   well-known that linear network coding [Li03] achieves the mulicast
   capacity.  BATS codes can benefit from network coding due to its
   inner code, but how to efficiently implement multicast needs further
   research.

4.2.  Protocol Design Issues

   The baseline scheme in this document focuses on the reliable
   communication.  There are other issues to be considered towards
   designing a fully functionally DDP based on a BATS coding scheme.
   Here we discuss some network management issues that are closely
   related to a BATS coding scheme: routing, congestion control and
   media access control.

   The outer code of a BATS code can be regarded as a channel code for
   the channel induced by the inner code, and hence the network
   management algorithms should try to maximize the capacity of the
   channel induced by the inner code.  A network utility maximization
   problem [Dong20] for BATS coding can be applied to study routing,
   congestion control and media access control jointly.  Compared with
   the network utility maximization for Internet, there are two major



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   differences.  First, the network flow rate is not measured by the
   rate of the raw packets.  Instead, a rank based measurement induced
   by the inner code is applied for BATS coding schemes.  Second, due to
   recoding, the raw packet rate of a flow may not be the same for
   different links, i.e., no flow conservation for BATS coding schemes.
   These differences affect both the objective and the constraints of
   the utility maximization problem.

   Practical congestion control, routing and media access control
   algorithms for BATS coding schemes deserve more research efforts.
   Due to the recoding operation, congestion control cannot be only
   performed end-to-end.  The rate of transmitting batches can be
   controlled end-to-end, but the number of recoded packets generated
   for a batch must be controlled at the intermediate nodes, which
   introduces new research issues for congestion control.  For routing,
   the BATS coding scheme is flexible for implementing multi-path data
   transmission, and different batches can be transmitted on a different
   path between a source node and a destination node.  Under the
   scenario of BATS coding schemes, media access control can have some
   different considerations: Retransmission is not necessary, and a
   reasonably high packet loss rate can be tolerated.

4.3.  Application Related Issues

   There are more researche issues pertaining to different applications.
   The reliable communication technique provided by BATS codes can be
   used for a broad range of network communication scenarios.  In
   general, a BATS coding scheme is suitable for data delivery in
   networks with multiple hops and unreliable links.

   One class of typical application scenario is wireless mesh and ad hoc
   networks [Toh02], including vehicular networks, wireless sensor
   networks, smart-lamppost networks, etc.  These networks are
   characterized by a large number of network devices connected
   wirelessly with each other without a centralized network
   infrastructure.  A BATS coding scheme is suitable for high data load
   delivery in such networks without the requirement that the point-to-
   point/one-hop communication is highly reliable.  Therefore, employing
   a BATS coding scheme can provide more freedom for media access
   control, including power control so that the overall network
   throughput can be improved.

   Another typical application scenario of BATS coding schemes is
   underwater acoustic networks [Sprea19], where the propagation delay
   of acoustic waves in underwater can be as long as several seconds.
   Due to the long delay, feedback based mechanisms become inefficient.
   Moreover, point-to-point/one-hop underwater acoustic communication
   (for both the forward and reverse directions) is highly unreliable.



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   Due to these reasons, traditional networking techinques developed for
   radio and wireline networks cannot be directly applied to underwater
   networks.  As a BATS coding scheme does not rely on the feedback for
   reliability communication and can tolerate highly unreliable links,
   it makes a good candidate for developing data delivery protocols for
   underwater acoustic networks.

   Last but not least, due to its capability of performing multi-source,
   multi-destination communications, a BATS coding scheme can be applied
   in various content distribution scenarios.  For example, a BATS
   coding scheme can be a candidate for the erasure code used in the
   liquid data networking framework [Byers20] of CCN (content centric
   networking), and provides the extra benefit of network coding
   [Zhang16].

5.  IANA Considerations

   This memo includes no request to IANA.

6.  Security Considerations

   Subsuming both Random Linear Network Codes (RLNC) and fountain codes,
   BATS codes naturally inherit both their desirable capability of
   offering confidentiality protection as well as their vulnerability
   towards pollution attacks.

6.1.  Provision of Confidentiality Protection

   Since the transported messages are linearly combined with random
   coefficients at each recoding node, it is statistically impossible to
   recover the individual messages by capturing the coded messages at
   any one or small number of nodes.  As long as the coding matrices of
   the transported messages cannot be fully recovered, any attempt of
   decoding any particular symbol of the transported messages is
   equivalent to random guessing [Bhattad05].

   The threat towards confidentiality, however, also exists in the form
   of eavesdropping on the initial encoding process, which takes place
   at the encoding nodes.  In these nodes, the transported data are
   presented in plain text and can be read along their transfer paths.
   Hence, information isolation between the encoding process and all
   other user processes running on the node must be assured.

   In addition, the authenticity and trustworthiness of the encoding,
   recoding and decoding program running on all the nodes must be
   attested by a trusted authority.  Such a measure is also necessary in
   countering pollution attacks.




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6.2.  Countermeasures against Pollution Attacks

   Like all network codes, BATS codes are vulnerable under pollution
   attacks.  In these attacks, one or more compromised coding node(s)
   can pollute the coded messages by injecting forged messages into the
   coding network and thus prevent the receivers from recovering the
   transported data correctly.

   The research community has long been investigating the use of various
   signature schemes (including homomorphic signatures) to identify the
   forged messages and stall the attacks (see [Zhao07], [Yu08],
   [Agrawal09]).  However, these countermeasures are regarded as being
   too computationally expensive to be employed in broadband
   communications.  Hence, a system-level approach based on Trusted
   Computing [TC-Wikipedia] is proposed as a practical alternative to
   protect BATS codes against pollution attacks.  This Trusted Computing
   based protection consists of the following countermeasures:

   1.  Attestation and Validation of all BATS encoding, recoding and
       decoding nodes in the network.  Remote attestation and repetitive
       validation of the identity and capability of these node based on
       valid public key certificates with proper authorization MUST be a
       pre-requisite for admitting these nodes to a network and
       permitting them to remain on that network.

   2.  Attestation of all encoding, recoding and decoding programs used
       in the coding nodes.  All programs used to perform the BATS
       encoding, recoding and decoding processes MUST be remotely
       attested before they are permitted to run on any of the coding
       nodes.  Reloading or alteration of programs MUST NOT be permitted
       during an encoding session.  Programs MUST be attested or
       validated again when they are executed in new execution
       environments instantiated even in the same node.

   3.  Original Authentication of all coded messages using network level
       security protocols such as IPsec or Peer Authentication over
       session-based communication using transport level security
       protocols such as TLS/DTLS MUST be employed in order to provide
       Message Origin or Communication Peer Authentication to every
       coded message sent through the coding network.

7.  References

7.1.  Normative References







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   [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>.

   [RFC8682]  Saito, M., Matsumoto, M., Roca, V., Ed., and E. Baccelli,
              "TinyMT32 Pseudorandom Number Generator (PRNG)", RFC 8682,
              DOI 10.17487/RFC8682, January 2020,
              <https://www.rfc-editor.org/info/rfc8682>.

7.2.  Informative References

   [Agrawal09]
              Agrawal, S. and D. Boneh, "Homomorphic MACs: MAC-based
              integrity for network coding", International Conference on
              Applied Cryptography and Network Security , 2009.

   [Bhattad05]
              Bhattad, K. and K. Narayanan, "Weakly Secure Network
              Coding", ISIT , 2007.

   [Byers20]  Byers, J. and M. Luby, "Liquid Data Networking", ICN ,
              2020.

   [Dong20]   Dong, Y., Jin, S., Yang, S., and H. Yin, "Network Utility
              Maximization for BATS Code enabled Multihop Wireless
              Networks", ICC , 2020.

   [Li03]     Li, S., Yeung, R., and N. Cai, "Linear Network Coding",
              IEEE Transactions on Information Theory , 2003.

   [RFC6330]  Luby, M., Shokrollahi, A., Watson, M., Stockhammer, T.,
              and L. Minder, "RaptorQ Forward Error Correction Scheme
              for Object Delivery", RFC 6330, DOI 10.17487/RFC6330,
              August 2011, <https://www.rfc-editor.org/info/rfc6330>.

   [Sprea19]  Sprea, N., Bashir, M., Truhachev, D., Srinivas, K.,
              Schlegel, C., and C. Claudio Sacchi, "BATS Coding for
              Underwater Acoustic Communication Networks", OCEANS ,
              2019.

   [TC-Wikipedia]
              "Trusted Computing",
              Wikipedia https://en.wikipedia.org/wiki/Trusted_Computing.

   [Toh02]    Toh, C., "Ad Hoc Mobile Wireless Networks", Prentice Hall
              Publishers , 2002.




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   [Yang14]   Yang, S. and R. Yeung, "Batched Sparse Codes", IEEE
              Transactions on Information Theory 60(9), 5322-5346, 2014.

   [Yang17]   Yang, S. and R. Yeung, "BATS Codes: Theory and Practice",
              Morgan & Claypool Publishers , 2017.

   [Yin19]    Yin, H., Tang, B., Ng, K., Yang, S., Wang, X., and Q.
              Zhou, "A Unified Adaptive Recoding Framework for Batched
              Network Coding", ISIT , 2019.

   [Yin20]    Yin, H., Yeung, R., and S. Yang, "A Protocol Design
              Paradigm for Batched Sparse Codes", Entroy , 2020.

   [Yu08]     Yu, Z., Wei, Y., Ramkumar, B., and Y. Guan, "An Efficient
              Signature-Based Scheme for Securing Network Coding Against
              Pollution Attacks", INFOCOM , 2008.

   [Zhang16]  Zhang, G. and Z. Xu, "Combing CCN with network coding: An
              architectural perspective", Computer Networks , 2016.

   [Zhao07]   Zhao, F., Kalker, T., Medard, M., and K. Han, "Signatures
              for content distribution with network coding", ISIT ,
              2007.

Appendix A.  Additional Stuff

Authors' Addresses

   Shenghao Yang
   CUHK(SZ)
   Shenzhen, Guangdong
   China

   Phone: +86 755 8427 3827
   Email: shyang@cuhk.edu.cn


   Xuan Huang
   CUHK
   Hong Kong, Hong Kong SAR
   China

   Phone: +852 3943 8375
   Email: 1155136647@link.cuhk.edu.hk







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   Raymond W. Yeung
   CUHK
   Hong Kong, Hong Kong SAR
   China

   Phone: +852 3943 8375
   Email: whyeung@ie.cuhk.edu.hk


   John K. Zao
   NCTU
   Hsinchu, Taiwan
   China

   Email: jkzao@ieee.org




































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