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Register a new userLDPC-Based Iterative Algorithm for Compression of Correlated Sources at Rates Approaching the Slepian-Wolf Bound
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Added by
Massimiliano Laddomada Ph.D.
Publication date
2007
fields
Informatics Engineering
and research's language is
English
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This article proposes a novel iterative algorithm based on Low Density Parity Check (LDPC) codes for compression of correlated sources at rates approaching the Slepian-Wolf bound. The setup considered in the article looks at the problem of compressing one source at a rate determined based on the knowledge of the mean source correlation at the encoder, and employing the other correlated source as side information at the decoder which decompresses the first source based on the estimates of the actual correlation. We demonstrate that depending on the extent of the actual source correlation estimated through an iterative paradigm, significant compression can be obtained relative to the case the decoder does not use the implicit knowledge of the existence of correlation.
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We present sufficient conditions for multicasting a set of correlated sources over cooperative networks. We propose joint source-Wyner-Ziv encoding/sliding-window decoding scheme, in which each receiver considers an ordered partition of other nodes. Subject to this scheme, we obtain a set of feasibility constraints for each ordered partition. We consolidate the results of different ordered partitions by utilizing a result of geometrical approach to obtain the sufficient conditions. We observe that these sufficient conditions are indeed necessary conditions for Aref networks. As a consequence of the main result, we obtain an achievable rate region for networks with multicast demands. Also, we deduce an achievability result for two-way relay networks, in which two nodes want to communicate over a relay network.
This paper deals with the problem of multicasting a set of discrete memoryless correlated sources (DMCS) over a cooperative relay network. Necessary conditions with cut-set interpretation are presented. A emph{Joint source-Wyner-Ziv encoding/sliding window decoding} scheme is proposed, in which decoding at each receiver is done with respect to an ordered partition of other nodes. For each ordered partition a set of feasibility constraints is derived. Then, utilizing the sub-modular property of the entropy function and a novel geometrical approach, the results of different ordered partitions are consolidated, which lead to sufficient conditions for our problem. The proposed scheme achieves operational separation between source coding and channel coding. It is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks, namely, Aref network and finite-field deterministic network. Also, in Gaussian cooperative networks, it is shown that reliable transmission of all DMCS whose Slepian-Wolf region intersects the cut-set bound region within a constant number of bits, is feasible. In particular, all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two-way relay networks.
The Slepian-Wolf bound on the admissible coding rate forms the most fundamental aspect of distributed source coding. As such, it is necessary to provide a framework with which to model more practical scenarios with respect to the arrangement of nodes in order to make Slepian-Wolf coding more suitable for multi-node Wireless Sensor Networks. This paper provides two practical scenarios in order to achieve this aim. The first is by grouping the nodes based on correlation while the second involves simplifying the structure using Markov correlation. It is found that although the bounds of these scenarios are more restrictive than the original Slepian-Wolf bound, the overall model and bound are simplified.
In this paper, we propose a polar coding based scheme for set reconciliation between two network nodes. The system is modeled as a well-known Slepian-Wolf setting induced by a fixed number of deletions. The set reconciliation process is divided into two phases: 1) a deletion polar code is employed to help one node to identify the possible deletion indices, which may be larger than the number of genuine deletions; 2) a lossless compression polar code is then designed to feedback those indices with minimum overhead. Our scheme can be viewed as a generalization of polar codes to some emerging network-based applications such as the package synchronization in blockchains. Some connections with the existing schemes based on the invertible Bloom lookup tables (IBLTs) and network coding are also observed and briefly discussed.
This paper is focused on the derivation of some universal properties of capacity-approaching low-density parity-check (LDPC) code ensembles whose transmission takes place over memoryless binary-input output-symmetric (MBIOS) channels. Properties of the degree distributions, graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information-theoretic bounds. These bounds are expressed in terms of the target block/ bit error probability and the gap (in rate) to capacity. Most of the bounds are general for any decoding algorithm, and some others are proved under belief propagation (BP) decoding. Proving these bounds under a certain decoding algorithm, validates them automatically also under any sub-optimal decoding algorithm. A proper modification of these bounds makes them universal for the set of all MBIOS channels which exhibit a given capacity. Bounds on the degree distributions and graphical complexity apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. The bounds are compared with capacity-approaching LDPC code ensembles under BP decoding, and they are shown to be informative and are easy to calculate. Finally, some interesting open problems are considered.
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