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GF(2^m) Low-Density Parity-Check Codes Derived from Cyclotomic Cosets

C. Tjhai·M. Tomlinson·R. Horan·M. Ambroze·M. Ahmed
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Abstract

Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2^m), where m>0 cyclic low-density parity-check codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this construction method is the ability to increment the code dimension by adding more idempotents and so steadily decrease the sparseness of the parity-check matrix. We show that the constructed codes can achieve performance very close to the sphere-packing-bound constrained for binary transmission.

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C. Tjhai, M. Tomlinson, R. Horan, M. Ambroze, M. Ahmed. 2005-07-23. GF(2^m) Low-Density Parity-Check Codes Derived from Cyclotomic Cosets. https://arxiv.org/abs/cs/0502037

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