Abstract: Low Density Parity Check Code (LDPC) is a kind of (n, k) linear block codes. The conventional encoding method can complete the encoding work when the length of the codes is short, but as the codes become longer, the memory of computer is hard to bear when still using the common encoding methods. To solve this problem, two kinds of effective encoding and decoding schemes were proposed. Firstly, different from the traditional data parity bit decoding, the proposed data reconciliation scheme used side information and syndrome produced by the initial data to employ joint decoding. Secondly, the parity matrix was stored in a way that only the positions of 1 in the form of the cross circular list were recorded, which could greatly save memory space. At last, C implementation could improve effectiveness of the codes. Length of a block of codes in this experiment was 105. The Bit Error Ratio (BER) of codes was converged above 1.0dB, only in need of 4 seconds to decode one block, the code rate could reach 24.85kb/s when the decoder was converged. The results show that the proposed schemes have strong timeliness.

Key words: Low Density Parity Check Code (LDPC), side information, syndrome, sparse matrix, reconciliation

摘要： 低密度奇偶校验码(LDPC)是一种(n,k)线性分组码。当分组码码长较短时，利用常规的编码方法可以完成编码工作。但随着分组码码长的增加，利用常规LDPC的编码方式编码，计算机的内存难以承担。为了解决以上问题，提出两种有效的编译码方案。首先，该数据协调方案不同于传统校验位译码，利用边信息和原始数据产生的校验子进行联合译码；其次，将校验矩阵以稀疏矩阵的形式存储，利用双向十字循环链表只记录1的位置的方式存储校验矩阵，这样可极大地节省内存空间；最后，通过C语言实现可提高编译码的有效性。实验中选取码长105的分组长度，译码器误码率(BER)收敛于1.0dB，每一分组译码时间仅需4s，译码收敛后速率达到24.85kb/s，时效性较强。

关键词: 低密度奇偶校验码, 边信息, 校验子, 稀疏矩阵, 数据协调