Syndrome-source-coding and its universal generalization

Ancheta, Jr. T.

doi:10.1109/tit.1976.1055578

Cited by 54 publications

(35 citation statements)

References 10 publications

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“…In light of the duality between source and channel coding (e.g., see [22]- [25] and other works), the results that we derived in this work can be directly applied to syndrome source coding with or without side information at the receiver. Our results extend similar work in [24].…”

Section: B Application To Syndrome Source Codingmentioning

confidence: 83%

On the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with Memory

Azar

Alajaji

2014

IEEE Trans. Commun.

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Abstract-We study the optimal maximum likelihood (ML) block decoding of general binary codes sent over two classes of binary additive noise channels with memory. Specifically, we consider the infinite and finite memory Polya contagion and queue-based channel models, which were recently shown to approximate well binary modulated correlated fading channels used with hard-decision demodulation. We establish conditions on the codes and channels parameters under which ML and minimum Hamming distance decoding are equivalent. We also present results on the optimality of classical perfect and quasi-perfect codes when used over the channels under ML decoding. Finally, we briefly apply these results to the dual problem of syndrome source coding with and without side information.Index Terms-Binary channels with finite and infinite memory, Markov noise, ML and minimum distance decoding, block codes, source-channel coding duality, syndrome source coding.

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Section: B Application To Syndrome Source Codingmentioning

confidence: 83%

On the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with Memory

Azar

Alajaji

2014

IEEE Trans. Commun.

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“…In particular, we point out that CS is identical to syndrome source coding [1] with linear codes over the real numbers. We propose and analyze new techniques for CS by adapting the construction and analysis of good codes for the q-ary symmetric channel [17], [12], [23].…”

Section: Discussionmentioning

confidence: 99%

“…A syndrome source coding system uses a linear code with parity-check matrix H ∈ F m×n to compress a vector x ∈ F n by computing its syndrome s = Hx [1]. Given a prior distribution on x, the decoder reconstructs x by maximizing Pr (x|s).…”

Section: B Connections With Coding Theorymentioning

confidence: 99%

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Compressed sensing and linear codes over real numbers

Zhang

Pfister

2008

2008 Information Theory and Applications Workshop

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Compressed sensing (CS) is a relatively new area of signal processing and statistics that focuses on signal reconstruction from a small number of linear (e.g., dot product) measurements. In this paper, we analyze CS using tools from coding theory because CS can also be viewed as syndrome-based source coding of sparse vectors using linear codes over real numbers. While coding theory does not typically deal with codes over real numbers, there is actually a very close relationship between CS and error-correcting codes over large discrete alphabets. This connection leads naturally to new reconstruction methods and analysis. In some cases, the resulting methods provably require many fewer measurements than previous approaches.

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“…As established in various degrees of generality in [6], [7], operational duality holds between linear lossless compression and linear encoding for channels with additive discrete noise. In that setup, the source realization is linearly transformed by the channel code parity-check matrix and the decompressor is the syndrome decoder of the channel code.…”

Section: B Operational Dualitymentioning

confidence: 99%

Operational duality between lossy compression and channel coding: Channel decoders as lossy compressors

Gupta¹,

Verdú²

2009

2009 Information Theory and Applications Workshop

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We explore the duality between lossy compression and channel coding in the operational sense: whether a capacityachieving encoder-decoder sequence achieves the rate distortion function of the dual problem when the channel decoder [encoder) is the source compressor [decompressor, resp). We show that, if used as a lossy compressor, the maximum-likelihood channel decoder of a randomly chosen capacity-achieving codebook achieves the rate-distortion function almost surely. However, operational duality does not hold for every capacity achieving encoderdecoder sequence. We show that there exist optimal channel coding schemes, which operate far from the rate-distortion function when used for the dual lossy compression problem.

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Syndrome-source-coding and its universal generalization

Cited by 54 publications

References 10 publications

On the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with Memory

On the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with Memory

Compressed sensing and linear codes over real numbers

Operational duality between lossy compression and channel coding: Channel decoders as lossy compressors

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