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

Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios

This paper treats point-to-point, multiple access and random access lossless source coding in the finite-blocklength regime. A random coding technique is developed, and its power in analyzing the third-order coding performance is demonstrated in all three scenarios. Results include a third-order-optimal characterization of the Slepian-Wolf rate region and a proof showing that for dependent sources, the independent encoders used by Slepian-Wolf codes can achieve the same third-order- optimal performance as a single joint encoder. The concept of random access source coding, which generalizes the multiple access scenario to allow for a subset of participating encoders that is unknown a priori to both the encoders and the decoder, is introduced. Contributions include a new definition of the probabilistic model for a random access-discrete multiple source, a general random access source coding scheme that employs a rateless code with sporadic feedback, and an analysis demonstrating via a random coding argument that there exists a deterministic code of the proposed structure that simultaneously achieves the third- order-optimal performance of Slepian-Wolf codes for all possible subsets of encoders

Zero-error Slepian-Wolf Coding of Confined Correlated Sources with Deviation Symmetry

In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes, Generalized Hamming Codes for Multiple Sources, to Matrix Partition Codes and use the latter to efficiently compress the target sources. We further show that every perfect or linear-optimal code is a Matrix Partition Code. We also present some conditions when Matrix Partition Codes are perfect and/or linear-optimal. Detail discussions of Matrix Partition Codes on Hamming sources are given at last as examples.Comment: submitted to IEEE Trans Information Theor

Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios

This paper treats point-to-point, multiple access and random access lossless source coding in the finite-blocklength regime. A random coding technique is developed, and its power in analyzing the third-order coding performance is demonstrated in all three scenarios. Via a connection to composite hypothesis testing, a new converse that tightens previously known converses for Slepian-Wolf source coding is established. Asymptotic results include a third-order characterization of the Slepian-Wolf rate region and a proof showing that for dependent sources, the independent encoders used by Slepian-Wolf codes can achieve the same third-order-optimal performance as a single joint encoder. The concept of random access source coding, which generalizes the multiple access scenario to allow for a subset of participating encoders that is unknown a priori to both the encoders and the decoder, is introduced. Contributions include a new definition of the probabilistic model for a random access source, a general random access source coding scheme that employs a rateless code with sporadic feedback, and an analysis demonstrating via a random coding argument that there exists a deterministic code of the proposed structure that simultaneously achieves the third-order-optimal performance of Slepian-Wolf codes for all possible subsets of encoders.Comment: 42 pages, 10 figures. Part of this work was presented at ISIT'1