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On the Minimum-Weight Codewords of Array LDPC Codes with Column Weight 4

刘海洋, 邓刚, Chang He

Published Nov 1, 2014• 0 citations
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In this paper, we present an algorithm to find all low-weight codewords in a given quasi-cyclic (QC) low-density parity-check (LDPC) code with a fixed column-weight and girth. The main idea is to view a low-weight codeword as an (a, 0) trapping sets, and then show that each topologically different (a, 0) trapping set can be dissected into smaller trapping sets. The proposed search method relies on the knowledge of possible topologies of such smaller trapping sets present in a code ensemble, which enables an efficient search. Combined with the high-rate QC LDPC code construction which successively adds blocks of permutation matrices, the algorithm ensures that in the code construction procedure all codewords up to a certain weight are avoided, which leads to a code with the desired minimum distance. The algorithm can be also used to determine the multiplicity of the low-weight codewords with different trapping set structure.

Information Theory and Applications Workshop (ITA)•Feb 1, 2013•8 citations
In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m,q), where q is an odd prime and m ≤ q. Using some analytical approaches, the lower bound on the number of minimum-weight codewords of C(m,q) given by Kaji (IEEE Int. Symp. Inf. Theory, June/July 2009) is proven to be tight for m = 4 and q > 19. In other words, C(4,q) has 4q2(q-1) minimum-weight codewords for all q > 19. In addition, we show some interesting universal properties of the supports of generators of minimum-weight codewords of the code C(4,q)(q > 19).
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.
In this paper, we present an algorithm to find all low-weight codewords in a given quasi-cyclic (QC) low-density parity-check (LDPC) code with a fixed column-weight and girth. The main idea is to view a low-weight codeword as an (a, 0) trapping sets, and then show that each topologically different (a, 0) trapping set can be dissected into smaller trapping sets. The proposed search method relies on the knowledge of possible topologies of such smaller trapping sets present in a code ensemble, which enables an efficient search. Combined with the high-rate QC LDPC code construction which successively adds blocks of permutation matrices, the algorithm ensures that in the code construction procedure all codewords up to a certain weight are avoided, which leads to a code with the desired minimum distance. The algorithm can be also used to determine the multiplicity of the low-weight codewords with different trapping set structure.