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arXiv:1106.2109 · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Analysis of Error Floors of Non-binary LDPC Codes over MBIOS Channel

T. Nozaki, Kenta Kasai, Kohichi Sakaniwa

Published Jan 1, 2011• 2 citations
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Abstract

In this paper, we investigate the error floors of non-binary low-density parity-check (LDPC) codes transmitted over the memoryless binary-input output-symmetric (MBIOS) channels. We provide a necessary and sufficient condition for successful decoding of zigzag cycle codes over the MBIOS channel by the belief propagation decoder. We consider an expurgated ensemble of non-binary LDPC codes by using the above necessary and sufficient condition, and hence exhibit lower error floors. Finally, we show lower bounds of the error floors for the expurgated LDPC code ensembles over the MBIOS channels.

DOI
10.1587/transfun.e94.a.2144

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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2012•1 citation
In this paper, we investigate the error floors of non-binary low-density parity-check (LDPC) codes transmitted over the memoryless binary-input output-symmetric (MBIOS) channels. We provide a necessary and sufficient condition for successful decoding of zigzag cycle codes over the MBIOS channel by the belief propagation decoder. We consider an expurgated ensemble of non-binary LDPC codes by using the above necessary and sufficient condition, and hence exhibit lower error floors. Finally, we show lower bounds of the error floors for the expurgated LDPC code ensembles over the MBIOS channels.
In this paper, we investigate the error floors of non-binary low-density parity-check (LDPC) codes transmitted over the memoryless binary-input output-symmetric (MBIOS) channels.We provide a necessary and sufficient condition for successful decoding of zigzag cycle codes over the MBIOS channel by the belief propagation decoder.We consider an expurgated ensemble of non-binary LDPC codes by using the above necessary and sufficient condition, and hence exhibit lower error floors.Finally, we show lower bounds of the error floors for the expurgated LDPC code ensembles over the MBIOS channels.
In this paper, we investigate the error floors of non-binary low-density parity-check (LDPC) codes transmitted over the memoryless binary-input output-symmetric (MBIOS) channels. We clarify a necessary and sufficient condition for successful decoding of zigzag cycle codes over the MBIOS channel by the BP decoder. We expurgate non-binary LDPC code ensemble to analyze and to lower the error floor by using the above condition. Finally, we show upper and lower bounds of the error floors of the expurgated LDPC code ensemble over the MBIOS channel.
In this paper, we propose a message passing decoding algorithm which lowers decoding error rates in the error floor regions for non-binary low-density parity-check (LDPC) codes transmitted over the binary erasure channel (BEC) and the memoryless binary-input output-symmetric (MBIOS) channels. In the case for the BEC, this decoding algorithm is a combination with belief propagation (BP) decoding and maximum a posteriori (MAP) decoding on zigzag cycles, which cause decoding errors in the error floor region. We show that MAP decoding on the zigzag cycles is realized by means of a message passing algorithm. Moreover, we extend this decoding algorithm to the MBIOS channels. Simulation results demonstrate that the decoding error rates in the error floor regions by the proposed decoding algorithm are lower than those by the BP decoder.
In this paper, we propose a message passing decoding algorithm which lowers decoding error rates in the error floor regions for nonbinary low-density parity-check (LDPC) codes transmitted over the binary erasure channel (BEC) and the memoryless binary-input output-symmetric (MBIOS) channels.In the case for the BEC, this decoding algorithm is a combination with belief propagation (BP) decoding and maximum a posteriori (MAP) decoding on zigzag cycles, which cause decoding errors in the error floor region.We show that MAP decoding on the zigzag cycles is realized by means of a message passing algorithm.Moreover, we extend this decoding algorithm to the MBIOS channels.Simulation results demonstrate that the decoding error rates in the error floor regions by the proposed decoding algorithm are lower than those by the BP decoder.
In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over general linear groups with those for non-binary LDPC codes over finite fields transmitted through the q-ary memoryless symmetric channels under belief propagation decoding.To analyze non-binary LDPC codes defined over both the general linear group GL(m, F 2 ) and the finite field F 2 m , we investigate non-binary LDPC codes defined over GL(m 3 , F 2 m 4 ).We propose a method to lower the error floors for non-binary LDPC codes.In this analysis, we see that the non-binary LDPC codes constructed by our proposed method defined over general linear group have the same decoding performance in the error floors as those defined over finite field.The non-binary LDPC codes defined over general linear group have more choices of the labels on the edges which satisfy the condition for the optimization.
In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over general linear groups with those for non-binary LDPC codes over finite fields transmitted through the q-ary memoryless symmetric channels under belief propagation decoding. To analyze non-binary LDPC codes defined over both the general linear group GL(m,F2)\mathrm{GL}(m,\mathbb{F}_2)GL(m,F2​) and the finite field F2m\mathbb{F}_{2^m}F2m​, we investigate non-binary LDPC codes defined over GL(m3,F2m4)\mathrm{GL}(m_3,\mathbb{F}_{2^{m_4}})GL(m3​,F2m4​​). We propose a method to lower the error floors for non-binary LDPC codes. In this analysis, we see that the non-binary LDPC codes constructed by our proposed method defined over general linear group have the same decoding performance in the error floors as those defined over finite field. The non-binary LDPC codes defined over general linear group have more choices of the labels on the edges which satisfy the condition for the optimization.