Lossless and near-lossless source coding for multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of correlated information sequences {X-i}(i=1)(infinity), and {Y-i}(i=1)(infinity) is drawn independent and identically distributed (i.i.d.) according to joint probability mass function (p.m.f.) p(x, y); the encoder for each source operates without knowledge of the other source; the decoder jointly decodes the encoded bit streams from both sources. The work of Slepian and Wolf describes all rates achievable by MASCs of infinite coding dimension (n --> infinity) and asymptotically negligible error probabilities (P-e((n)) --> 0). In this paper, we consider the properties of optimal instantaneous MASCs with finite coding dimension (n 0) performance. The interest in near-lossless codes is inspired by the discontinuity in the limiting rate region at P-e((n)) = 0 and the resulting performance benefits achievable by using near-lossless MASCs as entropy codes within lossy MASCs. Our central results include generalizations of Huffman and arithmetic codes to the MASC framework for arbitrary p(x, y), n, and P-e((n)) and polynomial-time design algorithms that approximate these optimal solutions

Optimal code design for lossless and near lossless source coding in multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of correlated information sequences {Xi}i=1∞ and {Yi }i=1∞ is drawn i.i.d. according to the joint probability mass function (p.m.f.) p(x,y); the encoder for each source operates without knowledge of the other source; the decoder jointly decodes the encoded bit streams from both sources. The work of Slepian and Wolf (1973) describes all rates achievable by MASCs with arbitrarily small but non-zero error probabilities but does not address truly lossless coding or code design. We consider practical code design for lossless and near lossless MASCs. We generalize the Huffman and arithmetic code design algorithms to attain the corresponding optimal MASC codes for arbitrary p.m.f. p(x,y). Experimental results comparing the optimal achievable rate region to the Slepian-Wolf region are included

Network vector quantization

We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples

Lossless source coding for multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of jointly distributed information sequences {Xi}i=1∞ and {Yi}i=1∞ is drawn i.i.d. according to joint probability mass function (p.m.f.) p(x,y); the encoder for each source operates without knowledge of the other source; the decoder receives the encoded bit streams of both sources. The rate region for MASCs with arbitrarily small but non-zero error probabilities was studied by Slepian and Wolf. In this paper, we consider the properties of optimal truly lossless MASCs and apply our findings to practical truly lossless and near lossless code design

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

The implementation of a lossless data compression module in an advanced orbiting system: Analysis and development

Data compression has been proposed for several flight missions as a means of either reducing on board mass data storage, increasing science data return through a bandwidth constrained channel, reducing TDRSS access time, or easing ground archival mass storage requirement. Several issues arise with the implementation of this technology. These include the requirement of a clean channel, onboard smoothing buffer, onboard processing hardware and on the algorithm itself, the adaptability to scene changes and maybe even versatility to the various mission types. This paper gives an overview of an ongoing effort being performed at Goddard Space Flight Center for implementing a lossless data compression scheme for space flight. We will provide analysis results on several data systems issues, the performance of the selected lossless compression scheme, the status of the hardware processor and current development plan

Broadcast Caching Networks with Two Receivers and Multiple Correlated Sources

The correlation among the content distributed across a cache-aided broadcast network can be exploited to reduce the delivery load on the shared wireless link. This paper considers a two-user three-file network with correlated content, and studies its fundamental limits for the worst-case demand. A class of achievable schemes based on a two-step source coding approach is proposed. Library files are first compressed using Gray-Wyner source coding, and then cached and delivered using a combination of correlation-unaware cache-aided coded multicast schemes. The second step is interesting in its own right and considers a multiple-request caching problem, whose solution requires coding in the placement phase. A lower bound on the optimal peak rate-memory trade-off is derived, which is used to evaluate the performance of the proposed scheme. It is shown that for symmetric sources the two-step strategy achieves the lower bound for large cache capacities, and it is within half of the joint entropy of two of the sources conditioned on the third source for all other cache sizes.Comment: in Proceedings of Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, November 201

Linear-Codes-Based Lossless Joint Source-Channel Coding for Multiple-Access Channels

A general lossless joint source-channel coding (JSCC) scheme based on linear codes and random interleavers for multiple-access channels (MACs) is presented and then analyzed in this paper. By the information-spectrum approach and the code-spectrum approach, it is shown that a linear code with a good joint spectrum can be used to establish limit-approaching lossless JSCC schemes for correlated general sources and general MACs, where the joint spectrum is a generalization of the input-output weight distribution. Some properties of linear codes with good joint spectra are investigated. A formula on the "distance" property of linear codes with good joint spectra is derived, based on which, it is further proved that, the rate of any systematic codes with good joint spectra cannot be larger than the reciprocal of the corresponding alphabet cardinality, and any sparse generator matrices cannot yield linear codes with good joint spectra. The problem of designing arbitrary rate coding schemes is also discussed. A novel idea called "generalized puncturing" is proposed, which makes it possible that one good low-rate linear code is enough for the design of coding schemes with multiple rates. Finally, various coding problems of MACs are reviewed in a unified framework established by the code-spectrum approach, under which, criteria and candidates of good linear codes in terms of spectrum requirements for such problems are clearly presented.Comment: 18 pages, 3 figure