构造速率兼容多元LDPC码的扩展方法

Extension method for constructing rate-compatible nonbinary LDPC codes

该文基于改进的扩展方法构造了一类速率兼容多元低密度校验（LDPC）码，其中低码率码的校验符号不仅与高码率码的码字有关，还与中间码率码的校验符号有关。构造过程涉及了掩模矩阵和基矩阵的优化设计、多元域元素的随机替换等具体步骤。该文还采用代数方法设计码的校验矩阵，进而降低了设计复杂度。所构造的码不仅具有速率兼容特性，还具有易于编译码器硬件实现的准循环结构。仿真结果表明：该码在较大的码率范围内都能够获得较好的瀑布区和平层区性能。

This paper describes a class of rate-compatible nonbinary low-density parity-check （LDPC） codes based on an improved extension method. The check symbols for lower code rates involve not only the codewords of the highest-rate code but also the check symbols of moderate-rate codes. The construction process optimizes the masking matrix and the base matrix with random replacement of nonbinary elements. This paper also describes an algebraic method to design the parity matrices to further reduce the design complexity. The codes are not only rate compatible, but also have a quasi-cycllc structure which will benefit hardware implementations of the encoder and decoder. Numerical tests show that the codes can achieve good performance within a wide range of code rates in both the waterfall region and in the error-floor region.