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Two-bit bit flipping algorithms for LDPC Codes and Collective Error Correction

IEEE TRANSACTIONS ON COMMUNICATIONS 2014年第4期62卷 1153-1163页

作者： Dung Viet Nguyen Vasic, Bane Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

A new class of bit flipping algorithms for low-density parity-check codes over the binary symmetric channel is proposed. Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its "strength." The introduction of this additional bit allows an increase in the guaranteed error correction capability. An additional bit is also employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis and selection of two-bit bit flipping algorithms is provided. The main component of this framework is the (re) definition of trapping sets, which are the most "compact" Tanner graphs that cause decoding failures of an algorithm. A recursive procedure to enumerate trapping sets is described. This procedure is the basis for selecting a collection of algorithms that work well together. It is demonstrated that decoders which employ a properly selected group of the proposed algorithms operating in parallel can offer high speed and low error floor decoding.

关键词： bit flipping algorithms low-density parity-check codes error floor trapping set

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On Trapping Sets and Guaranteed Error Correction Capability of LDPC Codes and GLDPC Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2010年第4期56卷 1600-1611页

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

The relation between the girth and the guaranteed error correction capability of left-regular low-density parity-check (LDPC) codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable node sets which expand by a factor of at least 3 gamma/4 is found based on the Moore bound. This bound, combined with the well known expander based arguments, leads to a lower bound on the guaranteed error correction capability. The decoding failures of the bit flipping algorithms are characterized using the notions of trapping sets and fixed sets. The relation between fixed sets and a class of graphs known as cage graphs is studied. Upper bounds on the guaranteed error correction capability are then established based on the order of cage graphs. The results are extended to left-regular and right-uniform generalized LDPC codes. It is shown that this class of generalized LDPC codes can correct a linear number of worst case errors (in the code length) under the parallel bit flipping algorithm when the underlying Tanner graph is a good expander. A lower bound on the size of variable node sets which have the required expansion is established.

关键词： bit flipping algorithms error correction capability fixed sets generalized low-density parity-check (LDPC) codes low-density parity-check (LDPC) codes 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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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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