TY - GEN

T1 - Analysis and enumeration of absorbing sets for non-binary graph-based codes

AU - Amiri, Behzad

AU - Kliewer, Jorg

AU - Dolecek, Lara

PY - 2013/12/19

Y1 - 2013/12/19

N2 - This work provides a generalization of absorbing sets for linear channel codes over non-binary alphabets. In a graphical representation of a non-binary channel code, an absorbing set can be described by a collection of topological and edge labeling conditions. In the non-binary case the equations relating neighboring variable and check nodes are over a non-binary field, and the edge weights are given by the non-zero elements of that non-binary field. As a consequence, it becomes more difficult for a given structure to satisfy the absorbing set constraints. This observation in part explains the superior performance of non-binary codes over their binary counterparts. We first show that, as the field order size increases, the ratio of trapping sets that satisfy the structural conditions of absorbing sets decreases. This suggests that a trapping set-only performance estimation of non-binary codes may not be as accurate in the error floor/high reliability regime. By using both insights from graph theory and combinatorial techniques, we establish the asymptotic distribution of non-binary elementary absorbing sets for regular code ensembles. Finally, we provide design guidelines for finite-length non-binary codes free of small absorbing sets.

AB - This work provides a generalization of absorbing sets for linear channel codes over non-binary alphabets. In a graphical representation of a non-binary channel code, an absorbing set can be described by a collection of topological and edge labeling conditions. In the non-binary case the equations relating neighboring variable and check nodes are over a non-binary field, and the edge weights are given by the non-zero elements of that non-binary field. As a consequence, it becomes more difficult for a given structure to satisfy the absorbing set constraints. This observation in part explains the superior performance of non-binary codes over their binary counterparts. We first show that, as the field order size increases, the ratio of trapping sets that satisfy the structural conditions of absorbing sets decreases. This suggests that a trapping set-only performance estimation of non-binary codes may not be as accurate in the error floor/high reliability regime. By using both insights from graph theory and combinatorial techniques, we establish the asymptotic distribution of non-binary elementary absorbing sets for regular code ensembles. Finally, we provide design guidelines for finite-length non-binary codes free of small absorbing sets.

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U2 - 10.1109/ISIT.2013.6620739

DO - 10.1109/ISIT.2013.6620739

M3 - Conference contribution

AN - SCOPUS:84890363738

SN - 9781479904464

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2815

EP - 2819

BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013

T2 - 2013 IEEE International Symposium on Information Theory, ISIT 2013

Y2 - 7 July 2013 through 12 July 2013

ER -