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International Symposium on Turbo Codes and Iterative Information Processing

Structural analysis of array-based non-binary LDPC codes

Shancheng Zhao, Xiujie Huang, Xiao Ma

Published Sep 1, 2016• 1 citation
Publisher

Abstract

Motivated by the superior performance of array-based non-binary low-density parity-check (LDPC) codes, we study in this paper their structural properties by combinational and graphical techniques. The main results are summarized as follows. First, we show that there exist codewords with symbol weight six and seven in array-based non-binary LDPC (NBLDPC) codes with column weight 3. Second, we characterize the graphical substructures induced by weight-6 and weight-7 codewords. Finally, we carry out comparisons to confirm the performance advantage of array-based NBLDPC codes.

DOI
10.1109/istc.2016.7593070

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Motivated by the superior performance of array-based non-binary low-density parity-check (LDPC) codes, we study in this paper their structural properties by combinational and graphical techniques. The main results are summarized as follows. First, we show that there exist codewords with symbol weight six and seven in array-based non-binary LDPC (NBLDPC) codes with column weight 3. Second, we characterize the graphical substructures induced by weight-6 and weight-7 codewords. Finally, we carry out comparisons to confirm the performance advantage of array-based NBLDPC codes.
Array‐based non‐binary (NB) low‐density parity‐check (LDPC) codes are attractive in practice for their advantages in implementation and performance. However, existing construction of array‐based NB LDPC codes is only with the prime number cases. In this Letter, the authors extend the array‐based construction to composite numbers to give an explicit construction of structured array‐based NB LDPC codes with column weights three, four, and five. The resulting codes have girth at least six. The simulation results show that the proposed structured codes perform as well as the random codes constructed by progressive edge‐growth algorithm, when decoded with the Q‐ary sum product algorithm and the low‐complexity weighted bit‐reliability‐based decoding algorithm.
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In this thesis we study Low Density Parity Check (LDPC) and LDPC like codes over \nnon-binary fields. We extend the concepts used for non-binary LDPC codes to generalize \nProduct Accumulate (PA) codes to non-binary fields. We present simulation results that \nshow that PA codes over GF(4) performs considerably better than binary PA codes at \nsmaller block lengths and slightly better at large block lengths. We also propose a trellis \nbased decoding algorithm to decode PA codes and show that its complexity is \nconsiderably lower than the message-passing algorithm. \nIn the second part of the thesis we study the convergence properties of non-binary PA \ncodes and non-binary LDPC codes. We use EXIT-charts to study the convergence \nproperties of non-binary LDPC codes with different mean column weights and show why \ncertain irregularities are better. Although the convergence threshold predicted by EXIT-charts \non non-binary LDPC codes is quite optimistic we can still use EXIT-charts for \ncomparison between non-binary LDPC codes with different mean column weights.