一类准循环LDPC码及其编码

A Class of Quasi-cyclic LDPC Codes and Encoding

针对空间通信的特点,对基于循环矩阵构造的一类正则准循环LDPC码进行了改进,得到了一类非正则准循环LDPC码。与原码相比,这类非正则LDPC码的奇偶校验矩阵H具有3个特点:行满秩,具有下三角结构,引入了一度变量节点。前两个特性使得这种LDPC码的编码计算复杂度和结构复杂度都与校验位长度成正比,从而便于编码器的软硬件实现。第三个特性使码的迭代译码门限稍有降低,但司时还能保证译码的收敛,计算机仿真结果也证明了这一点。本文还简化了对围长不小于6的条件的证明,推导了系统码校验位的计算公式,并在此基础上给出了利用移位寄存器的编码电路。

Firstly, based on the characters of space communication, this study improves a class of regular quasi-cyclic LDPC codes which is based on circulant matrices and obtains a kind of irregular quasi-cyclic LDPC codes. Compared with original codes, the parity check matrix called H of this irregular LDPC ensemble has three characters： 1. H is row full rank; 2. H is lower triangulation; 3. H contains degree one variable nodes. With the first two characters, the encoding complexity of computation and architecture of this kind of LDPC are proportion to the length of check symbols, so encoders implemented with software and hardware are quite simple. This feature is very important to deep space communication because the resource on board is constrained. The third character makes the iterative decoding threshold lower than the original codes. Moreover, the computer simulation has proved this result. Secondly, the proof for the condition of girth not shorter than 6 is simplifed compared to the original ones. Last, the computing formula is derived for parity check symbols of systemic codes. Based on this formula, the encoding circuit has been investigated using shift registers.