Proof of threshold saturation for spatially coupled sparse superposition codes

Barbier, Jean; Dia, Mohamad; Macris, Nicolas

doi:10.1109/isit.2016.7541484

Cited by 33 publications

(39 citation statements)

References 21 publications

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“…This base matrix construction was also used in [79] for SC-SPARCs. Other base matrix constructions can be found in [72,35,8,12].…”

Section: Spatially Coupled Sparc Constructionmentioning

confidence: 99%

“…SC-SPARC constructions generally have a 'seed' to jumpstart decoding. In [8], a small fraction of sections of β are fixed a priori -this pinning condition is used to analyze the state evolution equations via the potential function method. Analogously, in the construction in [12], additional rows are introduced in the design matrix for the blocks corresponding to the first row of the base matrix.…”

Section: Spatially Coupled Sparc Constructionmentioning

confidence: 99%

“…The state evolution recursion was analyzed for a certain class of spatially coupled SPARCs by Barbier et al [8] using the potential method introduced in [120,76,35]. It is shown in [8] that the fixed points of the state evolution recursion (5.8)-(5.9) coincide with the stationary points of a suitably defined potential function. This is then used to show 'threshold saturation' for spatially coupled SPARCs with AMP decoding, i.e., for all rates R < C, state evolution predicts vanishing probability of decoding error in the limit of large section size.…”

Section: Asymptotic State Evolution Analysismentioning

confidence: 99%

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Sparse Regression Codes

Venkataramanan

Tatikonda

Barron

2019

FNT in Communications and Information Theory

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Developing computationally-efficient codes that approach the Shannon-theoretic limits for communication and compression has long been one of the major goals of information and coding theory. There have been significant advances towards this goal in the last couple of decades, with the emergence of turbo codes, sparse-graph codes, and polar codes. These codes are designed primarily for discrete-alphabet channels and sources. For Gaussian channels and sources, where the alphabet is inherently continuous, Sparse Superposition Codes or Sparse Regression Codes (SPARCs) are a promising class of codes for achieving the Shannon limits.This monograph provides a unified and comprehensive over-view of sparse regression codes, covering theory, algorithms, and practical implementation aspects. The first part of the monograph focuses on SPARCs for AWGN channel coding, and the second part on SPARCs for lossy compression (with squared error distortion criterion). In the third part, SPARCs are used to construct codes for Gaussian multi-terminal channel and source coding models such as broadcast channels, multiple-access channels, and source and channel coding with side information. The monograph concludes with a discussion of open problems and directions for future work. v vi Chapter 1 A: β: 0, c 2 , 0, c L , 0, , 0 0, M columns M columns M columns Section 1 Section 2 Section L T n rows 0, c 1 , 0, 0, Figure 1.1: A Gaussian sparse regression codebook of block length n: A is a design matrix with independent Gaussian entries, and β is a sparse vector with one non-zero in each of L sections. Codewords are of the form Aβ, i.e., linear combinations of the columns corresponding to the non-zeros in β. The message is indexed by the locations of the non-zeros, and the values c 1 , . . . , c L are fixed a priori.

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“…This base matrix construction was also used in [79] for SC-SPARCs. Other base matrix constructions can be found in [72,35,8,12].…”

Section: Spatially Coupled Sparc Constructionmentioning

confidence: 99%

Section: Spatially Coupled Sparc Constructionmentioning

confidence: 99%

Section: Asymptotic State Evolution Analysismentioning

confidence: 99%

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Sparse Regression Codes

Venkataramanan

Tatikonda

Barron

2019

FNT in Communications and Information Theory

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“…In particular, we formulate the fixedlength distribution matching as a Bayesian inference problem. The formulation is inspired from the compressed sensing paradiagm [12,13] and sparse superposition (SS) codes [14][15][16][17]. Moreover, we provide a low-complexity algorithm based on generalized approximate message-passing (GAMP) [18,19] and spatial coupling.…”

Section: Introductionmentioning

confidence: 99%

A Compressed Sensing Approach for Distribution Matching

Dia

Aref

Schmalen

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from the compressed sensing paradigm and the sparse superposition (SS) codes. First, we introduce sparsity in the binary source via position modulation (PM). We then present a simple and exact matcher based on Gaussian signal quantization. At the receiver, the dematcher exploits the sparsity in the source and performs low-complexity dematching based on generalized approximate message-passing (GAMP). We show that GAMP dematcher and spatial coupling lead to an asymptotically optimal performance, in the sense that the rate tends to the entropy of the target distribution with vanishing reconstruction error in a proper limit. Furthermore, we assess the performance of the dematcher on practical Hadamardbased operators. A remarkable inherent feature of our proposed solution is the possibility to: i) perform matching at the symbol level (nonbinary); ii) perform joint channel coding and matching.

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“…This base matrix construction was also used in[16] for SC-SPARCs. Other base matrix constructions can be found in[7],[10],[13],[17].…”

mentioning

confidence: 99%

Spatially Coupled Sparse Regression Codes: Design and State Evolution Analysis

Hsieh

Rush

Venkataramanan

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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We consider the design and analysis of spatially coupled sparse regression codes (SC-SPARCs), which were recently introduced by Barbier et al. for efficient communication over the additive white Gaussian noise channel. SC-SPARCs can be efficiently decoded using an Approximate Message Passing (AMP) decoder, whose performance in each iteration can be predicted via a set of equations called state evolution. In this paper, we give an asymptotic characterization of the state evolution equations for SC-SPARCs. For any given base matrix (that defines the coupling structure of the SC-SPARC) and rate, this characterization can be used to predict whether AMP decoding will succeed in the large system limit. We then consider a simple base matrix defined by two parameters (ω, Λ), and show that AMP decoding succeeds in the large system limit for all rates R < C. The asymptotic result also indicates how the parameters of the base matrix affect the decoding progression. Simulation results are presented to evaluate the performance of SC-SPARCs defined with the proposed base matrix.

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Proof of threshold saturation for spatially coupled sparse superposition codes

Cited by 33 publications

References 21 publications

Sparse Regression Codes

Sparse Regression Codes

A Compressed Sensing Approach for Distribution Matching

Spatially Coupled Sparse Regression Codes: Design and State Evolution Analysis

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