Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes

Barbier, Jean; Krząkała, Florent

doi:10.1109/tit.2017.2713833

Cited by 109 publications

(184 citation statements)

References 57 publications

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“…The replica symmetric formula for the potential of random linear estimation was recently proved rigorously [8]. The proof of the SE equations of [18] for general signal distributions fixes a conjecture in the proof of [23] and shows that the replica symmetric formula holds true when the information vector m follows a block-iid distribution. In this work we study sums of K a SPARC signals.…”

Section: A Prior Work and Contributionmentioning

confidence: 99%

SPARCs and AMP for Unsourced Random Access

Fengler

Jung

Caire

2019

2019 IEEE International Symposium on Information Theory (ISIT)

103

104

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This paper studies the optimal achievable performance of compressed sensing based unsourced random-access communication over the real AWGN channel. "Unsourced" means, that every user employs the same codebook. This paradigm, recently introduced by Polyanskiy, is a natural consequence of a very large number of potential users of which only a finite number is active in each time slot. The idea behind compressed sensing based schemes is that each user encodes his message into a sparse binary vector and compresses it into a real or complex valued vector using a random linear mapping. When each user employs the same matrix this creates an effective binary inner multiple-access channel. To reduce the complexity to an acceptable level the messages have to be split into blocks. An outer code is used to assign the symbols to individual messages. This division into sparse blocks is analogous to the construction of sparse regression codes (SPARCs), a novel type of channel codes, and we can use concepts from SPARCs to design efficient random-access codes. We analyze the asymptotically optimal performance of the inner code using the recently rigorized replica symmetric formula for the free energy which is achievable with the approximate message passing (AMP) decoder with spatial coupling. An upper bound on the achievable rates of the outer code is derived by classical Shannon theory. Together this establishes a framework to analyse the trade-off between SNR, complexity and achievable rates in the asymptotic infinite blocklength limit. Finite blocklength simulations show that the combination of AMP decoding, with suitable approximations, together with an outer code recently proposed by Amalladinne et. al. outperforms state of the art methods in terms of required energy-per-bit at lower decoding complexity.

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Section: A Prior Work and Contributionmentioning

confidence: 99%

SPARCs and AMP for Unsourced Random Access

Fengler

Jung

Caire

2019

2019 IEEE International Symposium on Information Theory (ISIT)

103

104

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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%

“…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. In an (ω, Λ) base matrix, the fact that the number of rows in the base matrix exceeds the number of columns by (ω − 1) helps decoding start from both ends.…”

Section: Spatially Coupled Sparc Constructionmentioning

confidence: 99%

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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“…Also, recent work by Fengler, Jung, and Caire [10] draws a close connection between the sparse structure created by CCS and sparse regression codes (SPARCs) [11]- [13]. Therein, they leverage the CCS data structure, but pair it with a dense CS matrix (rather than the CCS block diagonal structure) and employ approximate message passing (AMP) [14], [15] to decode it.…”

Section: Introductionmentioning

confidence: 99%

An Enhanced Decoding Algorithm for Coded Compressed Sensing

Amalladinne

Chamberland

Narayanan

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to machine-type communications. Coded compressed sensing uses a divide-and-conquer approach to break the sparse recovery task into sub-components whose dimensions are amenable to conventional compressed sensing solvers. The recovered fragments are then stitched together using a low complexity decoder. This article introduces an enhanced decoding algorithm for coded compressed sensing where fragment recovery and the stitching process are executed in tandem, passing information between them. This novel scheme leads to gains in performance and a significant reduction in computational complexity. This algorithmic opportunity stems from the realization that the parity structure inherent to coded compressed sensing can be used to dynamically restrict the search space of the subsequent recovery algorithm.

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Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes

Cited by 109 publications

References 57 publications

SPARCs and AMP for Unsourced Random Access

SPARCs and AMP for Unsourced Random Access

Sparse Regression Codes

An Enhanced Decoding Algorithm for Coded Compressed Sensing

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