113 research outputs found
Low-Complexity Approaches to Slepian–Wolf Near-Lossless Distributed Data Compression
This paper discusses the Slepian–Wolf problem of distributed near-lossless compression of correlated sources. We introduce practical new tools for communicating at all rates in the achievable region. The technique employs a simple “source-splitting” strategy that does not require common sources of randomness at the encoders and decoders. This approach allows for pipelined encoding and decoding so that the system operates with the complexity of a single user encoder and decoder. Moreover, when this splitting approach is used in conjunction with iterative decoding methods, it produces a significant simplification of the decoding process. We demonstrate this approach for synthetically generated data. Finally, we consider the Slepian–Wolf problem when linear codes are used as syndrome-formers and consider a linear programming relaxation to maximum-likelihood (ML) sequence decoding. We note that the fractional vertices of the relaxed polytope compete with the optimal solution in a manner analogous to that observed when the “min-sum” iterative decoding algorithm is applied. This relaxation exhibits the ML-certificate property: if an integral solution is found, it is the ML solution. For symmetric binary joint distributions, we show that selecting easily constructable “expander”-style low-density parity check codes (LDPCs) as syndrome-formers admits a positive error exponent and therefore provably good performance
Multi-Way Relay Networks: Orthogonal Uplink, Source-Channel Separation and Code Design
We consider a multi-way relay network with an orthogonal uplink and
correlated sources, and we characterise reliable communication (in the usual
Shannon sense) with a single-letter expression. The characterisation is
obtained using a joint source-channel random-coding argument, which is based on
a combination of Wyner et al.'s "Cascaded Slepian-Wolf Source Coding" and
Tuncel's "Slepian-Wolf Coding over Broadcast Channels". We prove a separation
theorem for the special case of two nodes; that is, we show that a modular code
architecture with separate source and channel coding functions is
(asymptotically) optimal. Finally, we propose a practical coding scheme based
on low-density parity-check codes, and we analyse its performance using
multi-edge density evolution.Comment: Authors' final version (accepted and to appear in IEEE Transactions
on Communications
Density Evolution for the Design of Non-Binary Low Density Parity Check Codes for Slepian-Wolf Coding
International audienceIn this paper, we investigate the problem of designing good non-binary LDPC codes for Slepian-Wolf coding. The design method is based on Density Evolution which gives the asymptotic error probability of the decoder for given code degree distributions. Density Evolution was originally introduced for channel coding under the assumption that the channel is symmetric. In Slepian-Wolf coding, the correlation channel is not necessarily symmetric and the source distribution has to be taken into account. In this paper, we express the non-binary Density Evolution recursion for Slepian-Wolf coding. From Density Evolution, we then perform code degree distribution optimization using an optimization algorithm called differential evolution. Both asymptotic performance evaluation and finite-length simulations show the gain at considering optimized degree distributions for SW coding
How to Achieve the Capacity of Asymmetric Channels
We survey coding techniques that enable reliable transmission at rates that
approach the capacity of an arbitrary discrete memoryless channel. In
particular, we take the point of view of modern coding theory and discuss how
recent advances in coding for symmetric channels help provide more efficient
solutions for the asymmetric case. We consider, in more detail, three basic
coding paradigms.
The first one is Gallager's scheme that consists of concatenating a linear
code with a non-linear mapping so that the input distribution can be
appropriately shaped. We explicitly show that both polar codes and spatially
coupled codes can be employed in this scenario. Furthermore, we derive a
scaling law between the gap to capacity, the cardinality of the input and
output alphabets, and the required size of the mapper.
The second one is an integrated scheme in which the code is used both for
source coding, in order to create codewords distributed according to the
capacity-achieving input distribution, and for channel coding, in order to
provide error protection. Such a technique has been recently introduced by
Honda and Yamamoto in the context of polar codes, and we show how to apply it
also to the design of sparse graph codes.
The third paradigm is based on an idea of B\"ocherer and Mathar, and
separates the two tasks of source coding and channel coding by a chaining
construction that binds together several codewords. We present conditions for
the source code and the channel code, and we describe how to combine any source
code with any channel code that fulfill those conditions, in order to provide
capacity-achieving schemes for asymmetric channels. In particular, we show that
polar codes, spatially coupled codes, and homophonic codes are suitable as
basic building blocks of the proposed coding strategy.Comment: 32 pages, 4 figures, presented in part at Allerton'14 and published
in IEEE Trans. Inform. Theor
Information Reconciliation for High-Dimensional Quantum Key Distribution using Nonbinary LDPC codes
Information Reconciliation is an essential part of Quantum Key distribution
protocols that closely resembles Slepian-Wolf coding. The application of
nonbinary LDPC codes in the Information Reconciliation stage of a
high-dimensional discrete-variable Quantum Key Distribution setup is proposed.
We model the quantum channel using a -ary symmetric channel over which
qudits are sent. Node degree distributions optimized via density evolution for
the Quantum Key Distribution setting are presented, and we show that codes
constructed using these distributions allow for efficient reconciliation of
large-alphabet keys.Comment: 5 pages, 1 figure, submitted to International Symposium on Topics in
Codin
Source Coding with Side Information at the Decoder and Uncertain Knowledge of the Correlation
International audienceThis paper considers the problem of lossless source coding with side information at the decoder, when the correlation model between the source and the side information is uncertain. Four parametrized models representing the correlation between the source and the side information are introduced. The uncertainty on the correlation appears through the lack of knowledge on the value of the parameters. For each model, we propose a practical coding scheme based on non-binary Low Density Parity Check Codes and able to deal with the parameter uncertainty. At the encoder, the choice of the coding rate results from an information theoretical analysis. Then we propose decoding algorithms that jointly estimate the source vector and the parameters. As the proposed decoder is based on the Expectation-Maximization algorithm, which is very sensitive to initialization, we also propose a method to produce first a coarse estimate of the parameters
Distributed Compression and Squashed Entanglement
A single quantum state can be shared by many distant parties. In this thesis,
we try to characterize the information contents of such distributed states by
defining the multiparty information and the multiparty squashed entanglement,
two steps toward a general theory of multiparty quantum information. As a
further step in that direction, we partially solve the multiparty distributed
compression problem where multiple parties use quantum communication to
faithfully transfer their shares of a state to a common receiver. We build a
protocol for multiparty distributed compression based on the fully quantum
Slepian-Wolf protocol and prove both inner and outer bounds on the achievable
rate region. We relate our findings to previous results in information theory
and discuss some possible applications.Comment: M.Sc thesis submitted to the Physics department of McGill University,
107 pages, 14 figure
Slepian-Wolf Coding for Broadcasting with Cooperative Base-Stations
We propose a base-station (BS) cooperation model for broadcasting a discrete
memoryless source in a cellular or heterogeneous network. The model allows the
receivers to use helper BSs to improve network performance, and it permits the
receivers to have prior side information about the source. We establish the
model's information-theoretic limits in two operational modes: In Mode 1, the
helper BSs are given information about the channel codeword transmitted by the
main BS, and in Mode 2 they are provided correlated side information about the
source. Optimal codes for Mode 1 use \emph{hash-and-forward coding} at the
helper BSs; while, in Mode 2, optimal codes use source codes from Wyner's
\emph{helper source-coding problem} at the helper BSs. We prove the optimality
of both approaches by way of a new list-decoding generalisation of [8, Thm. 6],
and, in doing so, show an operational duality between Modes 1 and 2.Comment: 16 pages, 1 figur
Codage de sources avec information adjacente et connaissance incertaine des corrélations
Dans cette thèse, nous nous sommes intéressés au problème de codage de sources avec information adjacente au décodeur seulement. Plus précisément, nous avons considéré le cas où la distribution jointe entre la source et l'information adjacente n'est pas bien connue. Dans ce contexte, pour un problème de codage sans pertes, nous avons d'abord effectué une analyse de performance à l'aide d'outils de la théorie de l'information. Nous avons ensuite proposé un schéma de codage pratique efficace malgré le manque de connaissance sur la distribution de probabilité jointe. Ce schéma de codage s'appuie sur des codes LDPC non-binaires et sur un algorithme de type Espérance-Maximisation. Le problème du schéma de codage proposé, c'est que les codes LDPC non-binaires utilisés doivent être performants. C'est à dire qu'ils doivent être construits à partir de distributions de degrés qui permettent d'atteindre un débit proche des performances théoriques. Nous avons donc proposé une méthode d'optimisation des distributions de degrés des codes LDPC. Enfin, nous nous sommes intéressés à un cas de codage avec pertes. Nous avons supposé que le modèle de corrélation entre la source et l'information adjacente était décrit par un modèle de Markov caché à émissions Gaussiennes. Pour ce modèle, nous avons également effectué une analyse de performance, puis nous avons proposé un schéma de codage pratique. Ce schéma de codage s'appuie sur des codes LDPC non-binaires et sur une reconstruction MMSE. Ces deux composantes exploitent la structure avec mémoire du modèle de Markov caché.In this thesis, we considered the problem of source coding with side information available at the decoder only. More in details, we considered the case where the joint distribution between the source and the side information is not perfectly known. In this context, we performed a performance analysis of the lossless source coding scheme. This performance analysis was realized from information theory tools. Then, we proposed a practical coding scheme able to deal with the uncertainty on the joint probability distribution. This coding scheme is based on non-binary LDPC codes and on an Expectation-Maximization algorithm. For this problem, a key issue is to design efficient LDPC codes. In particular, good code degree distributions have to be selected. Consequently, we proposed an optimization method for the selection of good degree distributions. To finish, we considered a lossy coding scheme. In this case, we assumed that the correlation channel between the source and the side information is described by a Hidden Markov Model with Gaussian emissions. For this model, we performed again some performance analysis and proposed a practical coding scheme. The proposed scheme is based on non-binary LDPC codes and on MMSE reconstruction using an MCMC method. In our solution, these two components are able to exploit the memory induced by the Hidden Markov model.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF
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