On generalized low-density parity-check codes based on Hamming component codes

Lentmaier, Michael; Zigangirov, Kamil Sh.

doi:10.1109/4234.781010

Cited by 161 publications

(156 citation statements)

References 7 publications

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“…GLD codes are Tanner structures [1] with random permutations. The reader can find a detailed description of GLD codes in [2] [3][4] [5]. We are aware that practical applications and 1 The work of Ezio Biglieri was supported by the STREP project 'DA VINCI' within the 7th FP of the European Commission.…”

Section: Introductionmentioning

confidence: 99%

Generalized low-density codes with BCH constituents for full-diversity near-outage performance

Boutros

Zémor

Fàbregas

et al. 2008

2008 IEEE International Symposium on Information Theory

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Abstract-A new graph-based construction of generalized low density codes (GLD-Tanner) with binary BCH constituents is described. The proposed family of GLD codes is optimal on block erasure channels and quasi-optimal on block fading channels. Optimality is considered in the outage probability sense. A classical GLD code for ergodic channels (e.g., the AWGN channel, the i.i.d. Rayleigh fading channel, and the i.i.d. binary erasure channel) is built by connecting bitnodes and subcode nodes via a unique random edge permutation. In the proposed construction of full-diversity GLD codes (referred to as root GLD), bitnodes are divided into 4 classes, subcodes are divided into 2 classes, and finally both sides of the Tanner graph are linked via 4 random edge permutations. The study focuses on non-ergodic channels with two states and can be easily extended to channels with 3 states or more.

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Section: Introductionmentioning

confidence: 99%

Generalized low-density codes with BCH constituents for full-diversity near-outage performance

Boutros

Zémor

Fàbregas

et al. 2008

2008 IEEE International Symposium on Information Theory

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“…Particularly, the bit nodes connected to a check node are constrained to be codewords of (n, k) linear block codes such as Hamming codes, Bose-Chaudhuri-Hocquengham (BCH) codes or ReedSolomon codes. After their introduction by Tanner, generalized LDPC (GLDPC) codes remained largely unexplored until the work of Boutros et al [11] and Lentmaier and Zigangirov [12].…”

Section: Introductionmentioning

confidence: 99%

Approaching capacity at high rates with iterative hard-decision decoding

Jian

Pfister

Narayanan

2012

2012 IEEE International Symposium on Information Theory Proceedings

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Abstract-A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., nonbinary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially-coupled GLDPC codes with BCH component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution (DE).

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“…Various GLDPC codes achieve better performance at the cost of higher decoding complexity for moderate block lengths [14][15][16][17] . They are generated by replacing the parity check equations in a parity-check matrix of an LDPC code with many kinds of short length component codes.…”

Section: ⅰ Introductionmentioning

confidence: 99%

“…They are generated by replacing the parity check equations in a parity-check matrix of an LDPC code with many kinds of short length component codes. The examples of component codes are Hamming component codes [14] , Reed-Muller component codes [15] , and BCH and RS component codes [16] . Recently, GLDPC codes with BCC as component codes are reported [13] .…”

Section: ⅰ Introductionmentioning

confidence: 99%

Combined Horizontal-Vertical Serial BP Decoding of GLDPC Codes with Binary Cyclic Codes

Chung¹

2014

The Journal of Korea Information and Communications Society

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BSTRACTIt is well known that serial belief propagation (BP) decoding for low-density parity-check (LDPC) codes achieves faster convergence without any increase of decoding complexity per iteration and bit error rate (BER) performance loss than standard parallel BP (PBP) decoding. Serial BP (SBP) decoding, such as horizontal SBP (H-SBP) decoding or vertical SBP (V-SBP) decoding, updates check nodes or variable nodes faster than standard PBP decoding within a single iteration.In this paper, we propose combined horizontal-vertical SBP (CHV-SBP) decoding. By the same reasoning, CHV-SBP decoding updates check nodes or variable nodes faster than SBP decoding within a serialized step in an iteration. CHV-SBP decoding achieves faster convergence than H-SBP or V-SBP decoding. We compare these decoding schemes in details. We also show in simulations that the convergence rate, in iterations, for CHV-SBP decoding is about    of that for standard PBP decoding, while the convergence rate for SBP decoding is about    of that for standard PBP decoding. In simulations, we use recently proposed generalized LDPC (GLDPC) codes with binary cyclic codes (BCC).

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On generalized low-density parity-check codes based on Hamming component codes

Cited by 161 publications

References 7 publications

Generalized low-density codes with BCH constituents for full-diversity near-outage performance

Generalized low-density codes with BCH constituents for full-diversity near-outage performance

Approaching capacity at high rates with iterative hard-decision decoding

Combined Horizontal-Vertical Serial BP Decoding of GLDPC Codes with Binary Cyclic Codes

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