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Error Correction Capability of Column-Weight-Three LDPC Codes Under the gallager a algorithm-Part II

IEEE TRANSACTIONS ON INFORMATION THEORY 2010年第6期56卷 2626-2639页

作者： Chilappagari, Shashi Kiran Nguyen, Dung Viet Vasic, Bane Marcellin, Michael W. Marvell Semicond Inc Santa Clara CA 95054 USA Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

The relation between the girth and the error correction capability of column-weight-three LDPC codes under the gallager a algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girth g >= 10 can correct all error patterns with up to (g/2 - 1) errors in at most g/2 iterations of the gallager a algorithm. For codes with Tanner graphs of girth g <= 8, it is shown that girth alone cannot guarantee correction of all error patterns with up to (g/2-1) errors under the gallager a algorithm. Sufficient conditions to correct (g/2 - 1) errors are then established by studying trapping sets.

关键词： Error floor gallager a algorithm girth low-density parity-check (LDPC) codes trapping sets

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Error-Correction Capability of Column-Weight-Three LDPC Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2009年第5期55卷 2055-2061页

作者： Chilappagari, Shashi Kiran Vasic, Bane Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

In this paper, the error-correction capability of column-weight-three low-density parity-check (LDPC) codes when decoded using the gallager a algorithm is investigated. It is proved that a necessary condition for a code to correct all error patterns with up to k >= 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, it is shown that given any alpha > 0, there exists N such that for all n > N, no code in the ensemble of column-weight-three codes can correct all alpha n or fewer errors. The results are extended to the bit flipping algorithms.

关键词： Error-correction capability gallager a algorithm low-density parity-check (LDPC) codes Tanner graph trapping sets

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Girth of the Tanner Graph and Error Correction Capability of LDPC Codes

Girth of the Tanner Graph and Error Correction Capability of...

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46th Annual Allerton Conference on Communication, Control and Computing

作者： Chilappagari, Shashi Kiran Nguyen, Dung Viet Vasic, Bane Marcellin, Michael W. Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

ISBN: (纸本)9781424429257

We investigate the relation between the girth and the guaranteed error correction capability of gamma-left regular LDPC codes. For column-weight-three codes, we give upper and lower bounds on the number of errors correctable by the gallager a algorithm. For higher column weight codes, we find the number of variable nodes which are guaranteed to expand by a factor of at least 3 gamma/4, hence giving a lower bound on the guaranteed correction capability under the bit flipping (serial and parallel) algorithms. We also establish upper bounds by studying the sizes of smallest possible trapping sets.

关键词： Low-density parity-check codes gallager a algorithm bit flipping algorithms error correction capability

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Analysis of failures of decoders for LDPC codes

Analysis of failures of decoders for LDPC codes

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作者： Chilappagari, Shashi Kiran The University of Arizona

学位级别：Ph.D.

Ever since the publication of Shannon's seminal work in 1948, the search for capacity achieving codes has led to many interesting discoveries in channel coding theory. Low-density parity-check (LDPC) codes originally proposed in 1963 were largely forgotten and rediscovered recently. The significance of LDPC codes lies in their capacity approaching performance even when decoded using low complexity sub-optimal decoding algorithms. Iterative decoders are one such class of decoders that work on a graphical representation of a code known as the Tanner graph. Their properties have been well understood in the asymptotic limit of the code length going to infinity. However, the behavior of various decoders for a given finite length code remains largely unknown. An understanding of the failures of the decoders is vital for the error floor analysis of a given code. Broadly speaking, error floor is the abrupt degradation in the frame error rate (FER) performance of a code in the high signal-to-noise ratio domain. Since the error floor phenomenon manifests in the regions not reachable by Monte-Carlo simulations, analytical methods are necessary for characterizing the decoding failures. In this work, we consider hard decision decoders for transmission over the binary symmetric channel (BSC). For column-weight-three codes, we provide tight upper and lower bounds on the guaranteed error correction capability of a code under the gallager a algorithm by studying combinatorial objects known as trapping sets. For higher column weight codes, we establish bounds on the minimum number of variable nodes that achieve certain expansion as a function of the girth of the underlying Tanner graph, thereby obtaining lower bounds on the guaranteed error correction capability. We explore the relationship between a class of graphs known as cage graphs and trapping sets to establish upper bounds on the error correction capability. We also propose an algorithm to identify the most probable noise conf

关键词： Error floor gallager a algorithm Instantons LDPC codes Pseudo-codewords Trapping sets

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Girth of the Tanner Graph and Error Correction Capability of LDPC Codes

Girth of the Tanner Graph and Error Correction Capability of...

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Annual Allerton Conference on Communication, Control, and Computing

作者： Shashi Kiran Chilappagari Dung Viet Nguyen Bane Vasic Michael W. Marcellin Dept. of Electrical and Computer Eng. University of Arizona

ISBN: (纸本)9781424429257

We investigate the relation between the girth and the guaranteed error correction capability of γ-left regular LDPC codes. For column-weight-three codes, we give upper and lower bounds on the number of errors correctable by the gallager a algorithm. For higher column weight codes, we find the number of variable nodes which are guaranteed to expand by a factor of at least 3γ/4, hence giving a lower bound on the guaranteed correction capability under the bit flipping (serial and parallel) algorithms. We also establish upper bounds by studying the sizes of smallest possible trapping sets.

关键词： Low-density parity-check codes gallager a algorithm Bit flipping algorithms Error correction capability

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