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

Conference: TURBO - CODING - 2006 - 4th International Symposium on Turbo Codes & Related Topics; 6th International ITG-Conference on Source and Channel Coding
04/03/2006 - 04/07/2006 at Munich, Germany

Proceedings: TURBO - CODING - 2006

Pages: 6Language: englishTyp: PDF

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Tjhai, C.; Tomlinson, M.; Horan, R.; Ahmed, M.; Ambroze, M. (Fixed and Mobile Communications Research, University of Plymouth, PL4 8AA, United Kingdom)

Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2m), 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 close to the sphere-packing-bound constrained for binary transmission.