Internet Engineering Task Force S. Yang
Internet-Draft X. Huang
Intended status: Informational CUHK(SZ)
Expires: April 24, 2019 R.W. Yeung
CUHK
J. Zao
NCTU
October 21, 2018
BATS Coding Scheme for Multi-hop Data Transport
draft-yang-nwcrg-bats-00
Abstract
This document describe a BATS coding scheme for communication through
a multi-hop network. 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.
Status of This Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 3
2. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . 3
2.2. Data Partitioning and Padding . . . . . . . . . . . . . . 4
2.3. Data Delivery Procedures . . . . . . . . . . . . . . . . 4
2.3.1. Source Node Procedures . . . . . . . . . . . . . . . 4
2.3.2. Intermediate Node Procedures . . . . . . . . . . . . 5
2.3.3. Destination Node Procedures . . . . . . . . . . . . . 6
2.4. Recommendation for the Parameters . . . . . . . . . . . . 6
2.5. Example FDP Packets . . . . . . . . . . . . . . . . . . . 7
3. BATS Code Specification . . . . . . . . . . . . . . . . . . . 7
3.1. Background . . . . . . . . . . . . . . . . . . . . . . . 7
3.2. Outer Code Encoder . . . . . . . . . . . . . . . . . . . 7
3.3. Inner Code Encoder (Recoder) Recommendations . . . . . . 8
3.4. Decoder Recommendations . . . . . . . . . . . . . . . . . 8
4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 8
5. Security Considerations . . . . . . . . . . . . . . . . . . . 8
5.1. Provision of Confidentiality Protection . . . . . . . . . 8
5.2. Countermeasures against Pollution Attacks . . . . . . . . 9
6. References . . . . . . . . . . . . . . . . . . . . . . . . . 9
6.1. Normative References . . . . . . . . . . . . . . . . . . 9
6.2. Informative References . . . . . . . . . . . . . . . . . 10
Appendix A. Additional Stuff . . . . . . . . . . . . . . . . . . 10
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 10
1. Introduction
This document specifies a BATS code [BATS] scheme for data delivery
in multi-hop networks. The BATS code described here includes an
outer code and an inner code. The outer code is a matrix
generalization of the 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 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 BATSMonograph [BATSMonograph].
The BATS coding scheme can be applied in multi-hop networks formed by
many wireless communication links, which are inherently unreliable
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due to interference. Existing network protocols like TCP/IP use end-
to-end retransmission and store-and-forward at the relays, so that
packet loss would accumulate along the way.
The BATS coding scheme can be used for various data delivery
applications like file transmission, video streaming, 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].
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 described in this document can be used by a
Data Delivery Protocol (DDP) with the following procedures.
Encoding at a source node which has the data for transmission:
* The FDP 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 FDP forms and transmits the FDP packets using the batches
and the corresponding batch information.
Recoding at an intermediate node that does not need the data:
* The FDP extracts the batches and the corresponding batch
information from its received FDP packets.
* A BAST recoder generates recoded packets of a batch.
* The FDP forms and transmits FDP packets using the recoded
packets and the corresponding batch information.
Decoding at a destination node that needs the data:
* The FDP extracts the batches and the corresponding batch
information from its received FDP packets.
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* A BATS decoder tries to recover the transmitted data using the
received batches.
* The FDP sends the decoded data to the application that needs
the data.
2.2. Data Partitioning and Padding
Suppose that the FDP has F octets data for transmission. The
construction of source packets from the data depends on two
parameters K and T:
o K: the number of source packets.
o T: the size of a source packet, in octets.
If F is smaller than T*K, the data MUST be padded to have T*K octets,
so that the data can be partitioned into K source packets, each of
which has T octets.
2.3. Data Delivery Procedures
2.3.1. Source Node Procedures
A source node has the data for transmission. The FDP will first pad
and partition the data into K source packets, each containing T
octets. The FDP 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 The degree distribution (DD), optional.
o A sequence of batch IDs (ID[i],i=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 each batch ID, the encoder returns the FDP
o a sparse degree (d), and
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o M coded packets (X'[i],i=0,1,...,M-1), each containing T' octets.
Here T' = T + M*ceil(log2(q))/8.
The FDP will use the batches to form FDP packets to be transmitted to
other network nodes towards the destination nodes. The FDP MUST
deliver with each coded packet its
o sparse degree,
o batch ID and certain extra information so that any receiver of the
coded packets of the batch can know whether the coded packets are
in the same batch or not, and whether two different batches are
generated from the same data or not.
The FDP MUST deliver the following information to each recoder:
o batch size M, and
o recoding field size q.
The FDP MUST deliver the following information to each decoder:
o batch size M,
o recoding field size q,
o the data size F, and
o the number of source packet K.
The packet length information MUST be known by all the nodes.
2.3.2. Intermediate Node Procedures
An intermediate node does not need the data, but only helps to
deliver the data to the destination nodes. At an intermediate node,
the FDP only receives the FDP packets from the other network nodes,
and should be able to extract coded packets and the corresponding
batch information from these packets.
The FDP provides the recoder with the following information:
o the batch size M,
o the recoding field size q,
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o a number of received coded packets of the same batch, each
containing T' octets, and
o a number M' of recoded packets to be generated.
The recoder uses the information provided by the FDP to generate M'
recoded packets, each containing T' octets. The FDP uses the M'
recoded packets to form the FDP packets for transmitting.
2.3.3. Destination Node Procedures
A destination node needs the data transmitted by the source node. At
the destination node, the FDP receives FDP packets from the other
network nodes, and should be able to extract coded packets and the
corresponding batch information from these packets.
The FDP provides the decoder with the following information:
o F: number of octets in the data,
o M: batch size,
o q: recoding field size,
o K: number of source packets
o A sequence of batches 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
FDP, which will use the source packets to form the source data.
2.4. Recommendation for the Parameters
The recommendation for the parameters M, K, T, and T' is shown as
follows:
o M is 8, 16 or 32.
o q is 2, 4, 8, 16, 32, 64, 128 or 256.
o T' is not larger than the maximum coded packet payload size.
o T = T' - M*ceil(log2(q))/8.
o K = ceil(F/T).
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It is RECOMMENDED that K is at least 128. However, the encoder/
decoder SHALL support an arbitrary positive integer value of K.
2.5. Example FDP Packets
A FDP can form a FDP packet by appending a header and a footer to
each coded packets.
The header should include F, M, K, q, batch ID, and degree.
3. BATS Code Specification
3.1. Background
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.
Assume that a pseudo-random number generator Rand() is given.
3.2. Outer Code Encoder
Let b[0], b[1], ...,b[K-1] be the K source packets. A batch with
batch ID bID is generated in the following steps.
First, a degree DEG=DEG(bID) is sampled using the give degree
distribution and Rand() with the default seed. After that,
initialize Rand() with bID as the seed.
Second, using Rand() sample DEG packets among all the source packets.
Suppose the indices of the packets sampled are i_1, i_2, ..., i_DEG.
Third, sample a DEGxM generator matrix G.
Fourth, form the batch X = (b[i_1], b[i_2], ..., b[i_DEG])*G, where
each column is a coded packet of the batch.
Last, append coefficient vectors to the packets of the batches. Let
X[i], i=0,1,...,M-1, be the (i+1)th column of X. The coefficient
vector of X[i] is the (i+1)th column of the MxM identity matrix with
entries in GF(q), which can be represented by M*log2(q)/8 octets.
The coded packet X'[i] is formed by appending the coefficient vector
before X[i].
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3.3. Inner Code Encoder (Recoder) Recommendations
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 batch ID, sparse degree and coded packet
length.
3.4. Decoder Recommendations
The belief propagation decoding algorithm suggested in the BATS code
paper [BATS] is recommended.
4. IANA Considerations
This memo includes no request to IANA.
5. 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.
5.1. Provision of Confidentiality Protection
Since the transported messages are linearly combined with random
coefficients at each recoding node, it is statistically impossible to
recover 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 is equivalent to randomly guessing the transported messages.
Thus, with the use of BATS codes, information confidentiality
throughout the data transport process is assured.
The only thread towards confidentiality exists in the form of
eavesdropping onto 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 the pollution attacks.
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5.2. 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 or inject forged messages into the
coding network. These attacks can prevent the receivers from
recovering the transported data correctly. Although error detection
mechanisms can be put in place to prevent the receivers from getting
the wrong messages, detection and discard of the polluted messages
still constitute a form of denial-of-service (DoS) attack.
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 [Zhao07], Yu08
[Yu08], Agrawal09 [Agrawal09]). Nevertheless, these counter measures
are regarded as being computationally to expensive to be employed in
broadband communications. A practical approach to protect against
pollution attacks consists of the following system-level
countermeasures:
1. Attestation and Validation of all encoding, recoding and decoding
nodes in the network. Remote attestation and repetitive
validation of a node based on valid public key certificates with
proper authorization MUST be a pre-requisite of admitting that
node into a network and permitting it to remain in 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 nodes.
3. Original Authentication of all coded messages using network or
transport level secure protocols such as IP-sec or TLS/DTLS MUST
be used to provide Peer or Message Origin Authentication to every
coded message sent through the coding network.
6. References
6.1. 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>.
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6.2. Informative References
[Agrawal09]
S. Agrawal and D. Boneh, "Homomorphic MACs: MAC-based
integrity for network coding", International Conference on
Applied Cryptography and Network Security , 2009.
[BATS] S. Yang and R.W. Yeung, "Batched Sparse Codes", IEEE
Transactions on Information Theory 60(9), 5322-5346, 2014.
[BATSMonograph]
S. Yang and R.W. Yeung, "BATS Codes: Theory and Practice",
Morgan & Claypool Publishers , 2017.
[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>.
[Yu08] Z. Yu, Y. Wei, B. Ramkumar, and Y. Guan, "An Efficient
Signature-Based Scheme for Securing Network Coding Against
Pollution Attacks", NFOCOM , 2008.
[Zhao07] F. Zhao, T. Kalker, M. Medard, and K.J. Han, "Signatures
for content distribution with network coding", ISIT ,
2007.
Appendix A. Additional Stuff
This becomes an Appendix.
Authors' Addresses
Shenghao Yang
CUHK(SZ)
Shenzhen, Guangdong
China
Phone: +86 755 8427 3827
Email: shyang@cuhk.edu.cn
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Xuan Huang
CUHK(SZ)
Shenzhen, Guangdong
China
Phone: +86 755 8427 3814
Email: 115010159@link.cuhk.edu.cn
Raymond W. Yeung
CUHK
Hong Kong, Hong Kong SAR
China
Phone: +852 3943 8375
Email: whyeung@ie.cuhk.edu.hk
John Zao
NCTU
Hsinchu, Taiwan
China
Email: jkzao@ieee.org
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