Abstract:

In order to construct nonbinary low density parity check (LDPC) codes with good waterfall and error floor properties, a method to improve the minimum Hamming distance of a class of nonbinary quasi cyclic (QC) LDPC codes is presented. Two upper bounds on the minimum Hamming distance are derived for the nonbinary QC LDPC codes whose paritycheck matrices consist of weight 2 columns. A special base matrix design allowing linear encoding in a parallel manner is also proposed. In addition, the design principals are given, according to which, the parallel and efficiently encodable codes reaching the upper bound on the minimum Hamming distance can be developed. Simulation shows that the proposed codes have both good waterfall and error floor properties.

Key words: low density parity check code, nonbinary, minimum Hamming distance, quasi cyclic, efficient encoding