基于比特置信度的低复杂度多进制LDPC码译码算法

项目名称： 基于比特置信度的低复杂度多进制LDPC码译码算法

项目编号： No.U1530117

项目类型： 联合基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 黄勤

作者单位： 北京航空航天大学

项目金额： 66万元

中文摘要： 与二进制码相比，多进制LDPC码译码门限更小、收敛更快、错误平台更低，有显著的性能优势。但是，其译码算法需要占用大量的计算和存储资源，严重阻碍了其在通信和存储系统中的应用。因此，本项目拟基于置信度降阶的思想开展多进制LDPC码译码关键技术研究：1）针对高阶域校验节点运算复杂的难题，基于扩域与子域的代数关系，将高阶域的置信度降阶为二进制域的置信度，进而提出低复杂度高性能的基于比特置信度译码算法；2）分析由于符号相关性丢失导致比特置信度在多进制Tanner图传播时劣化的问题，利用比特汉明距离、符号重数、多重置信度平行传播和多子域置信度降阶的思想，进一步提升译码算法性能；3）基于有限域符号的约简矩阵表示，给出易于软硬件实现的高效分层式译码器。本项目的研究将为多进制LDPC码突破关键性技术障碍并走向应用进而提升通信和存储系统性能提供理论依据和技术支持。

中文关键词： 多进制LDPC码；译码算法；比特置信度

英文摘要： Compared with their binary counterparts, nonbinary LDPC codes over Galois fields have significant performance advantages, e.g., smaller decoding threshold, faster convergence rate, lower error-floor. However, their decoding algorithms need to consume overwhelming computational complexity and memory resources, which have become an obstacle for their applications in communication and storage systems. Thus, the project aims to study low-complexity decoding for nonbinary LDPC codes based on reliability decomposition: 1) in order to simplify the check-node computation in high-order extension fields, we will decompose high-order reliability into low-order reliability following the algebra relationship between extension field and subfield, and then derive the low-complexity high-performance decoding algorithm based on bit-reliability; 2) we will focus the degradation of bit-reliability during message-passing over nonbinary Tanner graph, and then compensate the degradation by bit Hamming distance, symbol plurality, multiple reliability-passing operations, and multi-subfield-reliability to further improve the performance of the proposed decoding algorithm; 4) to facilitate the soft or hardware implementation, we will give layered structure decoders from reduction matrices of Galois field elements. Overall, this project will overcome the most important obstacle in the application of nonbinary LDPC codes for communication and storage systems.

英文关键词： Nonbinary LDPC codes;Decoding algorithm;Bit-reliability