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A Deviation-Based Conditional Upper Bound on the Error Floor Performance for Min-Sum decoding of Short LDPC Codes

IEEE TRANSACTIONS ON COMMUNICATIONS 2012年第12期60卷 3567-3578页

作者： Psota, Eric T. Kowalczuk, Jedrzej Perez, Lance C. Univ Nebraska Dept Elect Engn Lincoln NE 68588 USA

Conditional upper bounds are given for min-sum decoding of low-density parity-check codes in the error floor region. It is generally thought that absorbing sets, i.e., small collections of variable nodes connected to a relatively small number of unsatisfied check nodes, are the primary source of errors in the error floor region. The conditional upper bounds presented here are based on the assumption that all error floor errors are caused by absorbing sets. In order to bound the probability of error associated with each absorbing set, a directed-edge Tanner graph is used to link absorbing sets to low-weight deviations. These low-weight deviations result when a proportionally large number of nodes within a stopping set belong to an absorbing set contained inside the stopping set. A complete collection of the most problematic absorbing sets, and the minimum deviation weights that result from them, are used to derive a conditional upper bound on the probability of error for min-sum decoding of low-density parity-check codes. Simulation results are given to demonstrate the accuracy of the bound.

关键词： LDPC codes iterative message-passing decoding stopping sets absorbing sets computation trees deviations

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LOCAL-OPTIMALITY GUARANTEES BASED ON PATHS FOR OPTIMAL decoding

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2013年第4期27卷 2049-2063页

作者： Even, Guy Halabi, Nissim Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded in the Tanner graph of the code. Local optimality implies both unique maximum likelihood optimality and unique linear programming (LP) decoding optimality. Also, an iterative message-passing decoding algorithm is guaranteed to find the unique locally optimal codeword if one exists. We demonstrate an instance of this proof technique by considering a definition of local optimality that is based on the simplest combinatorial structures in Tanner graphs, namely, paths of length h. We apply the technique of local optimality to binary Tanner codes (including any low-density parity-check code, and in particular any irregular repeat-accumulate code with both even and odd repetition factors). Inverse polynomial bounds in the code length are proved on the word error probability of LP decoding for binary Tanner codes. When the local codes are restricted to single parity-check codes, these bounds also hold for decoding by a certain iterative message-passing decoding algorithm.

关键词： coding theory Tanner codes local optimality maximum likelihood linear programming decoding error probability iterative message-passing decoding repeat-accumulate codes

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A Fast Double Layered decoding Algorithm for Quasi-Cyclic LDPC Codes

A Fast Double Layered Decoding Algorithm for Quasi-Cyclic LD...

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Pacific-Asia Conference on Circuits, Communications and Systems

作者： Chen, Zhixiong Yuan, Jinsha N China Elect Power Univ Sch Elect & Elect Engn Baoding 071003 Hebei Peoples R China

ISBN: (纸本)9780769536149

Most Quasi-Cyclic LDPC codes decoders of IEEE 802.11n and IEEE 802.16e standards adopt Layered decoding algorithm recently. A fast double layered decoding algorithm for Quasi-Cyclic LDPC codes in which two row groupings of check nodes are processed synchronously in order to speed the decoding processing is proposed. Compared to BP algorithm and normal Layered decoding algorithm, the proposed algorithm provides a faster decoding speed and more favorable tradeoffs among complexity, decoding speed and error correcting performance. Simulation results show validity and efficiency of the proposed decoding algorithm.

关键词： iterative message-passing decoding Quasi-Cyclic LDPC codes layered decoding IEEE 802.11n IEEE 802.16e

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Quantized iterative message passing Decoders with Low Error Floor for LDPC Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2014年第1期62卷 1-14页

作者： Zhang, Xiaojie Siegel, Paul H. Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA Univ Calif San Diego Ctr Magnet Recording Res La Jolla CA 92093 USA

The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures - variously referred to as near-codewords, trapping sets, absorbing sets, or pseudocodewords - in a Tanner graph representation of the code. Many approaches have been proposed to lower the error floor by designing new LDPC codes with fewer such substructures or by modifying the decoding algorithm. Using a theoretical analysis of iterative MP decoding in an idealized trapping set scenario, we show that a contributor to the error floors observed in the literature may be the imprecise implementation of decoding algorithms and, in particular, the message quantization rules used. We then propose a new quantization method - (q+1)-bit quasi-uniform quantization - that efficiently increases the dynamic range of messages, thereby overcoming a limitation of conventional quantization schemes. Finally, we use the quasi-uniform quantizer to decode several LDPC codes that suffer from high error floors with traditional fixed-point decoder implementations. The performance simulation results provide evidence that the proposed quantization scheme can, for a wide variety of codes, significantly lower error floors with minimal increase in decoder complexity.

关键词： Low-density parity-check (LDPC) codes iterative message-passing decoding sum-product algorithm message quantization error floors trapping sets

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Bounds on the Number of Iterations for Turbo-Like Ensembles Over the Binary Erasure Channel

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IEEE TRANSACTIONS ON INFORMATION THEORY 2009年第6期55卷 2602-2617页

作者： Sason, Igal Wiechman, Gil Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check (LDPC) codes and variations of repeat-accumulate codes). The transmission of the code ensembles is assumed to take place over a binary erasure channel, and the bounds refer to the asymptotic case where we let the block length tend to infinity. The simplicity of the bounds derived in this paper stems from the fact that they are easily evaluated and are expressed in terms of some basic parameters of the ensemble which include the fraction of degree-2 variable nodes, the target bit erasure probability, and the gap between the channel capacity and the design rate of the ensemble. This paper demonstrates that the number of iterations which is required for successful message-passing decoding scales at least like the inverse of the gap (in rate) to capacity, provided that the fraction of degree-2 variable nodes of these turbo-like ensembles does not vanish (hence, the number of iterations becomes unbounded as the gap to capacity vanishes).

关键词： Accumulate-repeat-accumulate (ARA) codes area theorem binary erasure channel (BEC) density evolution (DE) extrinsic information transfer (EXIT) charts iterative message-passing decoding low-density parity-check (LDPC) codes stability condition

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Analysis of Connections Between Pseudocodewords

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IEEE TRANSACTIONS ON INFORMATION THEORY 2009年第9期55卷 4099-4107页

作者： Axvig, Nathan Dreher, Deanna Morrison, Katherine Psota, Eric Perez, Lance C. Walker, Judy L. Univ Nebraska Dept Math Lincoln NE 68588 USA Univ Nebraska Dept Elect Engn Lincoln NE 68588 USA

The role of pseudocodewords in causing non-codeword outputs in linear programming decoding, graph cover decoding, and iterative message-passing decoding is investigated. The three main types of pseudocodewords in the literature-linear programming pseudocodewords, graph cover pseudocodewords, and computation tree pseudocodewords-are reviewed and connections between them are explored. Some discrepancies in the literature on minimal and irreducible pseudocodewords are highlighted and clarified, and the minimal degree cover necessary to realize a pseudocodeword is found. Additionally, some conditions for the existence of connected realizations of graph cover pseudocodewords are given. This allows for further analysis of when graph cover pseudocodewords induce computation tree pseudocodewords. Finally, an example is offered that shows that existing theories on the distinction between graph cover pseudocodewords and computation tree pseudocodewords are incomplete.

关键词： Graph cover decoding iterative message-passing decoding linear programming decoding low-density parity-check (LDPC) codes pseudocodewords

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On the Total Power Capacity of Regular-LDPC Codes With iterative message-passing Decoders

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2016年第2期34卷 375-396页

作者： Ganesan, Karthik Grover, Pulkit Rabaey, Jan Goldsmith, Andrea Stanford Univ Dept Elect Engn Stanford CA 94305 USA Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA

Motivated by recently derived fundamental limits on total (transmit + decoding) power for coded communication with VLSI decoders, this paper investigates the scaling behavior of the minimum total power needed to communicate over AWGN channels as the target bit-error-probability tends to zero. We focus on regular-LDPC codes and iterative message-passing decoders. We analyze scaling behavior under two VLSI complexity models of decoding. One model abstracts power consumed in processing elements (node model), and another abstracts power consumed in wires which connect the processing elements (wire model). We prove that a coding strategy using regular-LDPC codes with Gallager-B decoding achieves order-optimal scaling of total power under the node model. However, we also prove that regular-LDPC codes and iterative message-passing decoders cannot meet existing fundamental limits on total power under the wire model. Furthermore, if the transmit energy-per-bit is bounded, total power grows at a rate that is worse than uncoded transmission. Complementing our theoretical results, we develop detailed physical models of decoding implementations using post-layout circuit simulations. Our theoretical and numerical results show that approaching fundamental limits on total power requires increasing the complexity of both the code design and the corresponding decoding algorithm as communication distance is increased or error-probability is lowered.

关键词： Low-density parity-check (LDPC) codes iterative message-passing decoding Total power channel capacity Energy-efficient communication System-level power consumption Circuit power consumption VLSI complexity theory

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Choosing "green" codes by simulation-based modeling of implementations

Choosing "green" codes by simulation-based modeling of imple...

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IEEE Global Communications Conference (GLOBECOM)

作者： Ganesan, Karthik Wen, Yang Grover, Pulkit Goldsmith, Andrea Rabaey, Jan Univ Calif Berkeley Berkeley CA 94720 USA

ISBN: (纸本)9781467309219;9781467309202

How do we design an error correcting code and a corresponding decoding implementation to minimize not just the transmit power, but the sum of transmit and decoding power? Recent interest in this question has led to new fundamental results that show the traditional approach of designing the code and the decoder implementation in isolation can be suboptimal. However, joint design of codes and their corresponding decoder implementations can be hard simply because of the sheer number of possibilities for both, and the human effort often required in optimizing the decoder implementation for a given code. In this paper, we suggest taking a middle-path between analyzing theoretical models of decoding and building decoder implementations. Based on circuit simulations of power consumption of decoders for simple regular LDPC codes, we develop circuit models for the decoding power for larger and more complex (but still regular) LDPC codes. These models are then used to search for the best code and corresponding decoder (within a limited set) for a given communication distance and error probability.

关键词： Joint design of codes and decoders circuit models for decoding power system-level power consumption iterative message-passing decoding low-density parity-check (LDPC) codes

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Choosing "green" codes by simulation-based modeling of implementations

Choosing "green" codes by simulation-based modeling of imple...

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IEEE Global Communications Conference

作者： Karthik Ganesan Yang Wen Pulkit Grover Andrea Goldsmith Jan Rabaey University of California Stanford University

ISBN: (纸本)9781467309202

关键词： Joint design of codes and decoders Circuit models for decoding power System-level power consumption iterative message-passing decoding Low-density parity-check (LDPC) codes decoders decoding Codes Choose communication distance Error correction codes Circuit simulation low density parity check codes Transmitter power Error probability

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