Download Binary Soliton-Like Rateless Coding for the Y

Binary Soliton-Like Rateless Coding
for the Y-Network
Andrew Liau, ShahramYousefi, Senior Member, IEEE,
and Il-Min Kim Senior Member, IEEE
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 59, NO. 12, DECEMBER 2011
Outline
 Introduction
 System model
 Soliton-like rateless coding
 Simulation results
Introduction
 In today’s telecommunication applications, content can originate
from multiple sources and may travel through many transport nodes
to reach one or more receivers.
 Currently, intermediate nodes in a communications network
perform
 Buffer-and-forward (BF)
 Not an optimal strategy in the sense of overall network throughput
 Network coding (NC)
 Each transport node linearly combines packets received
 Provides the maximum throughput for all users simultaneously
 The complexity increases on the decoder side
LT code and Raptor code
 Provide practical capacity-achieving solutions by way of carefully-
designed encoding degree distributions
 The complexities for these rateless codes are very low (logarithmic
to linear scale).
 For multicast scenarios for the binary erasure channel (BEC)
 When the encoder uses the Robust Soliton Distribution (RSD)
 Capacity over the BEC is achieved universally
 The erasure rate of the channel does not need to be known a priori
 The original LT codes provide optimality for single-source, single-
hop, and single-sink networks.
Motivation
 We want a scheme that has good information diffusion
 Using a channel code providing Maximum Distance Separable (MDS)
-type (every coded bit is the same) properties
 Loss resilience
 NC linearly combines packets at intermediate nodes
 Fountain codes linearly combine packets at the sources and provides
low decoding complexity
 Advantages of marrying NC and fountain codes
 The low complexity decoder
 The ability to increase the effective length of the fountain code
Previous works
[8] R. Gummadi and R. S. Sreenivas, “Relaying a fountain code across
multiple nodes,” in Proc. ITW, 2008, pp. 49–153.
 [8] describes a system where encoding is superimposed at each
transport node resulting in multi-layer fountain coding.
 The performance of the code is equivalent to a single hop as the RSD is
preserved.
 Multi-layer fountain decoding might be impractical to use due to its high
complexity.
 LT Network Codes [4]
[4] M. Champel, K. Huguenin, A. Kermarrec, and N. Le Scouarnec, “LT
network codes,” in Proc. ICDCS, 2010.
 Generalizing the setting to any network with a single source and sink.
 Using complex data structures, transport nodes selectively combine
packets to form the RSD at each hop.
 NP-hard problem at each transport node
 Other shortcomings
 Not resilient to nodes churn rates
 Not scalable (complexity and dependencies on the network configurations)
System model
 Soliton-like degree distribution
 Allowing each source to use the RSD regardless of the number of total
sources.
 We consider a two-user, two-hop , single-sink network.(Y-network)
System model
 At each source (S1 and S2): The information is encoded by an LT
code.
 At the relay (𝑅): Either BF or NC is performed.
 At the sink (𝐷): After successful decoding, the sink transmits a
single acknowledgment (ACK) bit indicating the termination of
the session.
System model
 Each
performs LT coding [5]
 Over the sets
 To produce the packets
 R:
 If NC is applied, re-encode
and
to generate
 If BF is applied , forwards packets from S1 in even time slots and
packets from S2 in odd time slots.
System model
 A key component of a fountain code is the packet degree distribution,
which characterizes the decoding efficiency and throughput
optimality.
 RSD
Soliton-like rateless coding
 RSD :
 The literature scale poorly with network size
 Sensitive to node churn rates
 =>SLRC
 With the RSD at each source , we need a intelligent NC at R to
preserve important properties of the RSD.
 => NC at R
Some attributes of the best distribution

𝑝(⋅) is an aggregate degree distribution seen from D.
 The probability of degree-two packet is the maximum of the
distribution
 =>
 =>
 =>

(fountain code ,in single-source, single-hop)
(in more practical scenarios)
For BP decoding to start, degree-one packets are required
 =>
 =>
(too many of them cause inefficient decoding)
 p(1)<<p(2) (Otherwise , distributions result in significantly larger
minimum overhead)
Soliton-like distribution
Soliton-like rateless coding : At R
 We protect degree-one and two packets by forwarding them with
probability λ ,where λ will be optimized.
 If the packets are not forwarded by R, then they are buffered for
future use.
 The memory of R is restricted to K for each source.
 R is restricted to form a new packet by combining a single packet
from S1 with a single packet from S2.
 Although a Soliton-like distribution is generated at R, redundancy
must also be addressed.
Soliton-like rateless coding
Soliton-like rateless coding
 Definition 3 (Soliton-like rateless coding (SLRC)):
 The SLRC protocol requires LT coding at each source
 Combining at R according to Algorithm 1 where
and
are
innovative.
 This means that Algorithm 1 reuses a packet
or more than
once only if there are no unused packets in the corresponding
buffers.
Soliton-like rateless coding
 Theorem 1: The aggregate distribution produced by the SLRC with
𝜆 ≥ 0.67 is Soliton-like.
 Proof :
 We can determine the degree distribution, 𝜇(𝑘), seen at 𝐷 from
the set of packets forwarded from either source:

𝑞(𝑘) is the probability of a packet of degree k being forwarded:
 The degree distribution,
,of innovative buffered S1 packets will
be:
 Where
and
are the probabilities that a packet of degree
one and two are not forwarded, respectively:
 When a packet is not forwarded, the relay distribution due to only
linear combining is :
 The aggregate distribution in
is a mixture of forwarded and
linearly combined packets :
 The probability, 𝜃, that a packet is from either distribution is defined
as :
Soliton-like distribution
Since the RSD is
used at each source
 4) : is satisfied when 𝜆≥ 0.67 ( By letting
 => 5)
 6) : Satisfied at each source encodes
 =>
 =>
also satisfies
maintains 6)
)
Soliton-like distribution
 Corollary 1: The aggregate distribution produced by the SLRC
protocol in the presence of a single source in a session is the RSD.
 Proof: Suppose that S2 has left the network. In this case, R can assume
that only degree-zero packets have been received from S2.
which results in the aggregate distribution being equal to the
RSD.
Simulation results
[9] S. Puducheri, J. Kliewer, and T. E. Fuja, “The design and performance of
distributed LT codes,” IEEE Trans. Inf. Theory, vol. 53, no. 10, pp.
3740–3754, Oct. 2007.
 The DLT [9]code is based on the RSD :
 With values of 𝑐, 𝛿, and a message length of 2K
 The proposed SLRC :
 With values of 𝑐, 𝛿, and a message length of K
 The SDLT [10]:
 With values of 𝑐, 𝛿, and a message length of K
 A coding distribution, Λ(𝑥), at R
 BF
[10] D. Sejdinovic, R. Piechocki, and A. Doufexi, “AND-OR tree analysis
of distributed LT codes,” in Proc. ITW, 2009, pp. 261–265.
 With K =100, an optimum value of 𝜆 = 0.95 was found for
SLRC.
Simulation results
Simulation results
Simulation results
Conclusion
 We propose a scheme that exploits the benefits of network coding
and fountain coding
 SLRC
 Not affected by node churn rates in that if a source node left, no
changes to the protocol are needed.
 By preserving key properties of the RSD as packets travel through
the network, we show that the aggregate distribution is Solitonlike
 Better at reliable success rates when compared to the DLT and
SDLT codes.