NWCRG S. Yang
Internet-Draft CUHK(SZ)
Intended status: Informational X. Huang
Expires: 4 June 2022 R. W. Yeung
CUHK
J. K. Zao
NCTU
1 December 2021
BATS Coding Scheme for Multi-hop Data Transport
draft-irtf-nwcrg-bats-02
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. This document is a product
of the Coding for Efficient Network Communications Research Group
(NWCRG).
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Copyright Notice
Copyright (c) 2021 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 4
2. A Use Case of BATS Coding Scheme . . . . . . . . . . . . . . 4
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . 5
2.2. Data Delivery Procedures . . . . . . . . . . . . . . . . 6
2.2.1. Source Node Data Partitioning and Padding . . . . . . 6
2.2.2. Source Node Outer Code Encoding Procedure . . . . . . 7
2.2.3. Recoding Procedures . . . . . . . . . . . . . . . . . 9
2.2.4. Destination Node Procedures . . . . . . . . . . . . . 9
2.3. Recommendation for the Parameters . . . . . . . . . . . . 10
2.4. Coding Parameters in DDP Packets . . . . . . . . . . . . 11
2.4.1. Coding Parameter Format . . . . . . . . . . . . . . . 11
2.4.2. Coded Packet Format . . . . . . . . . . . . . . . . . 12
3. BATS Code Specification . . . . . . . . . . . . . . . . . . . 13
3.1. Common Parts . . . . . . . . . . . . . . . . . . . . . . 13
3.2. Outer Code Encoder . . . . . . . . . . . . . . . . . . . 14
3.3. Inner Code Encoder (Recoder) . . . . . . . . . . . . . . 15
3.4. Outer Code Decoder . . . . . . . . . . . . . . . . . . . 16
4. Research Issues . . . . . . . . . . . . . . . . . . . . . . . 17
4.1. Coding Design Issues . . . . . . . . . . . . . . . . . . 17
4.2. Protocol Design Issues . . . . . . . . . . . . . . . . . 18
4.3. Application Related Issues . . . . . . . . . . . . . . . 19
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 20
6. Security related Considerations . . . . . . . . . . . . . . . 20
6.1. Preventing Eavesdropping . . . . . . . . . . . . . . . . 20
6.2. Countermeasures against Pollution Attacks . . . . . . . . 21
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 22
7.1. Normative References . . . . . . . . . . . . . . . . . . 22
7.2. Informative References . . . . . . . . . . . . . . . . . 22
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 24
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 24
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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
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 clearer towards a
sophisticated BATS code based network protocol. Important research
directions include the security issues, congestion control and
routing algorithms for BATS codes, etc.
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This document is a product of and represents the collaborative work
and consensus of the Coding for Efficient Network Communications
Research Group (NWCRG); it is not an IETF product and is not an IETF
standard.
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].
2. A Use Case of BATS Coding Scheme
The BATS coding scheme described in this document can be used, for
example, by a Data Delivery Protocol (DDP). Though this document is
not about a DDP, we briefly illustrate in this section how a BATS
coding scheme is employed by a DDP to make the role of the coding
scheme clear. Some terms that will be used in this section are
summarized here:
* DDP: data delivery protocol.
* DDP packet: the packet formed by a DDP employing a BATS coding
scheme.
* source packet: the packet formed by the data for delivery.
* outer encoder: the outer code encoder of a BATS code.
* recoder: the inner code encoder of a BATS code.
* outer decoder: the outer code decoder of a BATS code.
* coded packet: the packet generated by the outer code encoder or a
recoder.
* batch: a set of coded packets generated by a BATS coding scheme
from the same subset of the source packets.
* recoded packet: a coded packet generated by a recoder.
* degree: the number of source packets used to generate a batch by
the outer encoder. The degree can be different for different
batch.
Other common terms can be found in RFC 8406 [RFC8406].
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2.1. Introduction
We describe a data delivery process that involves one source node,
one destination node, and multiple intermediate nodes in between. A
BATS coding scheme includes an outer code encoder (also called outer
encoder), an inner code encoder (also called recoder), and an outer
decoder which decodes the outer code and the inner code jointly as
illustrated in Figure 1. The functions of the outer encoder, recoder
and outer decoder are described below:
|
| {set of source packets}
v
+-+-+-+-+-+-+-+-+
| outer encoder |
| v | source node
| recoder |
+-+-+-+-+-+-+-+-+
|
| {set of DDP packets}
v
+-+-+-+-+-+-+-+-+
| |
| recoder | intermediate node
| |
+-+-+-+-+-+-+-+-+
|
| {set of DDP packets}
v
...
|
| {set of DDP packets}
v
+-+-+-+-+-+-+-+-+
| |
| outer decoder | destination node
| |
+-+-+-+-+-+-+-+-+
|
| {set of source packets}
v
Figure 1: A network model for data delivery.
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At the source node, the DDP first processes the data to be delivered
into a number of source packets each of the same number of bits (see
details in Section 2.2.1), and then provides all the source packets
to the outer encoder. The outer encoder will further generate a
sequence of batches, each consisting of a fixed number of coded
packets (see the description in Section 2.2.2).
Each batch generated at the source node is further processed by the
recoder separately. The recoder may generate a number of new coded
packets using the existing coded packets of the batch (see the
description in Section 2.2.3). After processed by the recoder, the
DDP forms and transmits the DDP packets using the coded packets,
together with the corresponding batch information.
We assume that a DDP packet is either correctly received or
completely erased during the communication. The DDP extracts the
coded packets and the corresponding batch information from its
received DDP packets. A recoder is employed at an intermediate node
that does not need the data, and generates recoded packets for each
batch (see the description in Section 2.2.3). The DDP forms and
transmits DDP packets using the recoded packets and the corresponding
batch information.
The outer decoder is employed at the destination node that needs the
data. The DDP extracts the coded packets and the corresponding batch
information from its received DDP packets. The outer decoder tries
to recover the transmitted data using the received batches (see the
description in Section 2.2.4). 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 coding parameters to be discussed in this
section, and will be calculated at the end of this section.
2.2.1. Source Node Data Partitioning and Padding
The DDP first determines the following parameters:
* Batch size (M): the number of coded packets in a batch generated
by the outer encoder.
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* Recoding field size (q): the number of elements in the finite
field for recoding. q is 2 or 2^8
* 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: the number of octets of a coefficient vector, calculated as O =
ceil(M*log2(q)/8), which is also called the coefficient vector
overhead.
* T: the number of data octets of a coded packet, calculated as T =
TO - 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 octets, 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 insertion process is shown in Figure 2.
Z = T - P
j = 1
v = 1
Let bl be the last source packet b[K-1]
for i = Z, Z+1, ..., T-1 do
bl[i] = j
if i+1 >= v+Z do
j += 1
v += j
Figure 2: Data Padding Insertion Process
2.2.2. Source Node Outer Code Encoding Procedure
The DDP provides the BATS encoder with the following information:
* Batch size (M): the number of coded packets in a batch.
* Recoding field size (q): the number of elements in the finite
field for recoding.
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* Maximum degree (MAX_DEG): a positive integer that specifies the
largest degree can be used.
* Degree distribution (DD): an unsigned integer array of size
MAX_DEG+1. The i-th entry DD[i] is the possibility that i is
chosen as the degree, where i is between 0 and MAX_DEG.
* A sequence of batch IDs (BID) (j, j = 0, 1, ...).
* Number of source packets (K).
* Packet size (T): the number of octets in a source packet.
* Source packets (b[i], i = 0, 1, ..., K-1).
Using this information, the outer encoder generates M coded packets
for each batch ID using the following steps to be described in
details at Section 3.2:
* Obtain a degree d by sampling DD. Roughly, the value d is chosen
with probability DD[d].
* Choose d source packets uniformly at random from all the K source
packets. It is allowed that a source packet is used by mutiple
batches.
* Generate M coded packets using the d source packets.
The DDP receives from the outer encoder a sequence of batches, where
the batch with ID j has
* a degree d[j], and
* 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 with its
* BID: batch ID
The DDP MUST deliver the following information to each recoder:
* M: batch size M
* q: recoding field size
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The DDP MUST deliver the following information to each decoder:
* M: batch size
* q: recoding field size
* K: the number of source packets
* 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.
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. If the DDP choose not to recode, it just forwards the
DDP packets it received. Otherwise, the DDP should be able to
extract coded packets and the corresponding batch information from
these packets.
For a received batch, the DDP determines a positive integer Mr, the
number of recoded packets to be transmitted for the batch, and
provides the recoder with the following information:
* the batch size M,
* the recoding field size q,
* a number of received coded packets of the same batch, each
containing TO octets, and
* the number of recoded packets to be generated (Mr).
The recoder uses the information provided by the DDP to generate Mr
recoded packets, each containing TO octets, to be described in
Section 3.3. 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 an
intermediate network node, and should be able to extract coded
packets and the corresponding batch information from these packets.
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The DDP provides the outer decoder (to be described in Section 3.4)
with the following information:
* M: batch size,
* q: recoding field size,
* K: the number of source packets
* T: the number of octets of a source packet
* A sequence of batches, each of which is formed by a number of
coded packets belonging to the same batch, with their
corresponding BIDs and degrees.
The decoder uses this information to decode the outer code and the
inner code jointly and recover 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 deletion 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 3: Data Padding Deletion Process
2.3. Recommendation for the Parameters
The recommendation for the parameters M and q is shown as follows:
* When q=2, M=16,32,64,128
* When q=256, M=4,8,16,32
It is RECOMMENDED that K is at least 128. The encoder/decoder SHALL
support an arbitrary positive integer value less than 2^16. However,
the BATS coding scheme to be described is not optimized for small K.
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2.4. Coding Parameters in DDP Packets
Here we provide an example of embedding the aforementioned BATS
coding parameters into the DDP packets which will be used for
recoding and decoding. A DDP can form a DDP packet using a coded
packet by adding necessary information that can help to deliver the
DPP packet to the next node, e.g., the DDP protocol version,
addresses and session identifiers. We will not go into the details
of formatting these fields in a DDP packet, but focus on how to
format the coding parameters and the coded packet in a DDP packet.
2.4.1. Coding Parameter Format
Here we provide an example of using 32 bits (4 octets) to embed the
parameters K, M, q, and BID. The 32 bits are separated into three
subfields, denoted as K, Mq and BID, respectively, as illustrated 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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| K | Mq | BID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 4: Coding parameter field format.
* K: 16-bit unsigned integer, specifying the number of source
packets of the BATS session.
* Mq: 3-bit unsigned integer to specify the value of M and q as
Table 1.
* BID: 13-bit unsigned integer, specifying the batch ID of the batch
the packet belongs to.
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+=====+=====+=====+
| Mq | M | q |
+=====+=====+=====+
| 000 | 16 | 2 |
+-----+-----+-----+
| 010 | 32 | 2 |
+-----+-----+-----+
| 100 | 64 | 2 |
+-----+-----+-----+
| 110 | 128 | 2 |
+-----+-----+-----+
| 001 | 4 | 256 |
+-----+-----+-----+
| 011 | 8 | 256 |
+-----+-----+-----+
| 101 | 16 | 256 |
+-----+-----+-----+
| 111 | 32 | 256 |
+-----+-----+-----+
Table 1: Values of Mq
field
The choice of the coding parameters depends on the computation cost,
the network conditions and the expected end-to-end coding
performance. Usually, a larger batch size M will have a better
coding performance, but higher computation cost for encoding,
recoding and decoding. The field size q affects the coefficient
vector overhead, and also the computation cost for recoding. Within
a BATS session, the BID field should be different for all batches,
and hence the maximum number of batches can be generated for the
outer encoder is 2^13. For different BATS sessions, batches can use
the same BID.
2.4.2. Coded Packet Format
O T
+-----------------------+-------------------------------+
| coefficient vector | coded data |
+-----------------------+-------------------------------+
Figure 5: Code packet format in a DDP packet.
A coded packet has TO octets, where the first O octets contain the
coefficient vector and the remaining T octets contain the coded data.
.
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* coefficient vector: O = M*log2(q)/8 octets. For the values of M
and q in Table 1, O is at most 32 octets when q is 256 and 6
octets when q is 2.
* coded data: T octets. T should be chosen so that the whole DDP
packet is at most PMTU.
Using the above formation, we can calculate the largest file size F
for different parameters. For example, when q=2 and M=128, we have O
= 6 octets. Counting the 4 octets for embedding the coding
parameters, we can choose T = PMTU-H-10, where H is the header length
of a DDP packet. As K can be at most 2^16-1, F can be at most (PMTU-
H-10)(2^16-1) octets. In this case, K/M is about 2^9 and the BID
field allows transmitting 2^4*K/M batches.
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). The O octets of coefficient vector are treated
as a column vector of O elements in GF(q), where q=2 or q=256.
Linear algebra and matrix operations over finite fields are assumed
in this section.
For two elements of GF(2), their multiplication corresponds to a
logical AND operation and their addition is an logical XOR operation.
An element of the field GF(256) can be represented by a polynomial
with binary coefficients and degree lower or equal to 7. The
addition between two elements of GF(256) is defined as the addition
of the two binary polynomials. The multiplication between two
elements of GF(256) is the multiplication of the two binary
polynomials modulo a certain irreducible polynomial of degree 8,
called a primitive polynomial. One example of such a primitive
polynomial for GF(256) is:
x^8 + x^4 + x^3 + x^2 + 1
A common primitive polynomial should be specified for all the finite
field multiplications over GF(256). Note that a binary polynomial of
degree less than 8 can be represented by a binary sequence of 8 bits,
i.e., an octet.
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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
3.2. Outer Code Encoder
Define a function called DegreeSampler that returns 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. Note that when K
< MAX_DEG, the degree value returned by DegreeSampler does not
exactly follow the distribution DD, which however would not affect
the practical decoding performance for the outer decoder to be
described in Section 3.4.
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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.
* Obtain a degree d by calling DegreeSampler with input j.
* Obtain idx and G[j] by calling BatchSampler with input j and d.
* 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.
* 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
3.3. Inner Code Encoder (Recoder)
In general, the inner code of a BATS code comprises (random) linear
network coding applied on the coded packets belonging to the same
batch. The recoded packets have the same BID. Suppose that coded
packets xr[i], i = 0, 1, ..., r-1, which have the same BID j, have
been received at an intermediate node, and Mr recoded packets are
supposed to be generated. Following traditional random linear
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network coding, a recoded packet can be generated by random linear
combination: (randomly) choose a sequence of coefficients c[i], i =
0, 1, ..., r-1 from GF(q), and generate
c[0]xr[0]+c[1]xr[1]+...+c[r-1]xr[r-1] as a recoded packet. This
recoding approach, called random linear recoding, achieves good
network coding performance for multicast when the batch size is
sufficiently large.
For unicast communications in a single path as illustrated in
Figure 1, it is not necessary to generate all the Mr recoded packets
using random linear combination. Instead, xr[i], i = 0, 1, ..., r-1,
are directly used as recoded packets, and max(Mr-r,0) recoded packets
are generated using linear combinations. Compared with random linear
recoding, this recoding approach, called systematic recoding, can
reduce both the computation cost and also the recoding latency that
accumulates linearly with the number of nodes. Note that the use of
systematic recoding may not always achieve the optimal network coding
performance as random linear recoding in more complicated
communication scenarios that include multiple paths and multiple
destination nodes.
3.4. Outer Code 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). For successful
decoding, we require that the total rank of all the batches is at
least K.
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.
We first 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:
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* Decoding step: Find a batch j that is decodable. Solve the
corresponding system of linear equations Y[j] = B[j]G[j]H[j] and
decode B[j].
* Substitution step: Substitute the decoded source packets into
undecodable batches. Suppose that a decoded source packet b[k] is
used in generating an 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.
When the degree distribution DD in the outer code encoder (see
Section 3.2) is properly designed, the BP decoder guarantees a high
probability for the recovery of a given fraction of the source
packets when K is large. 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 BP decoder stops which may happen with a high
probability when K is relatively small, it is possible to continue
with inactivation decoding, where certain source packets are treated
inactive so that a similar belief propagation process can be resumed.
The reader is referred to RFC 6330 [RFC6330] for the design of a
precode with a good inactivation decoding performance.
4. Research Issues
The baseline BATS coding scheme described in Section 2 and Section 3
needs various refinement and complement towards becoming 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
When the number of batches is sufficiently large, the BATS code
specification in Section 3 has nearly optimal performance in the
sense that the decoding can be successful with a high probability
when the total rank of all the batches used for decoding is just
slightly larger than the number of source packet K. 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.
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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 called 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 reliable
communication. There are other issues to be considered towards
designing a fully functional 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
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
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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 research 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.
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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.
Due to these reasons, traditional networking techniques 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 related Considerations
Subsuming both random linear network codes (RLNC) and fountain codes,
BATS codes naturally inherit both their desirable security capability
of preventing eavesdropping, as well as their vulnerability towards
pollution attacks. In this section, we discuss some related research
issues.
6.1. Preventing Eavesdropping
Suppose that an eavesdropper obtains a batch where the degree value d
is strictly larger than the batch size M. Even the eavesdropper has
all the related encoding information, the system of linear equations
related to this batch does not have a unique solution, and the
probability that the eavesdropper can guess the d source packets used
for encoding the batch correctly is 2^(d-M)T>=2^T (see also
[Bhattad05]). When inactivation decoding is applied, we can design
the degree distribution DD so that the smallest degree is M+1, and
hence prevent the eavesdropper from decoding source packets from
individual batches.
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If we allow the eavesdropper to collect multiple batches and use
inactivation decoding, the same security holds if the total rank of
all the batches collected by the eavesdropper is less than the number
of source packet. Therefore, if the DDP can manage to restrict the
eavesdropper from collecting a sufficiently number of coded packets,
the native security of BATS code is effective when T is sufficiently
large. Here by native security, we mean the security protection
provided by the BATS coding scheme without extra enhancement.
If the eavesdropper can collect a sufficient number of coded packets
for correct decoding, the native security of BATS code is
ineffective. To prevent eavesdropping in this case, one research
direction is to encrypt some of the crucial information used in
decoding. Such information can be, for example, the batch ID and the
batch generator matrix. The security level of such schemes needs
further evaluations.
The threat exists for 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 source
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.
6.2. Countermeasures against Pollution Attacks
Like all network codes, BATS codes are vulnerable to pollution
attacks. In these attacks, one or more compromised coding node(s)
can pollute the coded messages by injecting forged packets into the
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 packets 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:
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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. Origin 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 Integrity or Origin Authentication to every coded packet
sent through the coding network.
7. References
7.1. 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>.
[RFC8406] Adamson, B., Adjih, C., Bilbao, J., Firoiu, V., Fitzek,
F., Ghanem, S., Lochin, E., Masucci, A., Montpetit, M-J.,
Pedersen, M., Peralta, G., Roca, V., Ed., Saxena, P., and
S. Sivakumar, "Taxonomy of Coding Techniques for Efficient
Network Communications", RFC 8406, DOI 10.17487/RFC8406,
June 2018, <https://www.rfc-editor.org/info/rfc8406>.
[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
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[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.R. Narayanan, "Weakly Secure Network
Coding", ISIT , 2007.
[Byers20] Byers, J.W. and M. Luby, "Liquid Data Networking", ICN ,
2020.
[Dong20] Dong, Y., Jin, S., Yang, S., and H.H.F. Yin, "Network
Utility Maximization for BATS Code enabled Multihop
Wireless Networks", ICC , 2020.
[Li03] Li, S.-Y.R., Yeung, R.W., 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.V.,
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.K., "Ad Hoc Mobile Wireless Networks", Prentice
Hall Publishers , 2002.
[Yang14] Yang, S. and R.W. Yeung, "Batched Sparse Codes", IEEE
Transactions on Information Theory 60(9), 5322-5346, 2014.
[Yang17] Yang, S. and R.W. Yeung, "BATS Codes: Theory and
Practice", Morgan & Claypool Publishers , 2017.
[Yin19] Yin, H.H.F., Tang, B., Ng, K.H., Yang, S., Wang, X., and
Q. Zhou, "A Unified Adaptive Recoding Framework for
Batched Network Coding", ISIT , 2019.
[Yin20] Yin, H.H.F., Yeung, R.W., and S. Yang, "A Protocol Design
Paradigm for Batched Sparse Codes", Entroy , 2020.
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[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.J. Han,
"Signatures for content distribution with network coding",
ISIT , 2007.
Acknowledgments
The authors would like to thank the NWCRG chairs, Vincent Roca (our
shepherd) and Marie-Jose Montpetit; and all those who provided
comments -- namely (in alphabetical order), Emmanuel Lochin, David
Oran, and Colin Perkins.
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
Raymond W. Yeung
CUHK
Hong Kong
Hong Kong SAR,
China
Phone: +852 3943 8375
Email: whyeung@ie.cuhk.edu.hk
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John K. Zao
NCTU
Hsinchu
Taiwan,
China
Email: jkzao@ieee.org
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