一种基于有限域的二进制和多进制空间耦合LDPC码构造方法

An Approach for Constructing Binary and Nonbinary Spatially-Coupled LDPC Codes Based on Finite Fields

空间耦合LDPC (Spatially-Coupled LDPC, SC-LDPC)码由于阈值饱和特性,被证明是未来无线通信系统的有力候选码型。SC-LDPC码是一种卷积LDPC码,在二元无记忆对称信道下采用置信传播算法时具有逼近香农限的性能。本文提出了一种构造二进制和多进制空间耦合LDPC码的统一方法。基于有限域GF(q)上的本原元、加法子群、乘法子群,构造了6类二进制和多进制空间耦合准循环LDPC码(Spatially-Coupled Quasi­Cyclic LDPC, SC-QC-LDPC),用此构造的LDPC码的围长至少为6。

Spatially-coupled LDPC codes are demonstrated to strong candidates for future optical communications systems due to the threshold saturating property. Spatially-coupled LDPC code is a kind of convolutional LDPC code. It has the performance of approaching Shannon limit when using belief propagation decoding algorithm in binary memoryless symmetric channel. A unified approach for constructing binary and nonbinary spatially-coupled LDPC codes is presented in this paper. Six classes of binary and nonbinary spatially-coupled Quasi-Cyclic LDPC codes are constructed based on primitive elements, additive subgroups, multiplicative subgroups of finite fields. Moreover, the girth of these codes is greater than or equal to 6.