低密度奇偶校验码加权大数逻辑译码研究

A Research on Weighted Majority-Logic Decoding for LDPC Codes

针对低密度奇偶校验(LDPC)码加权大数逻辑(WMLG)译码物理意义问题,提出了一种基于最大对数最大后验概率(max-log MAP)译码的推导方法。该方法利用幂求和的对数近似表达式给出信息位的对数似然比(LLR),理论证明了WMLG译码与max-log MAP译码的等价性。仿真结果也进一步表明,与MAP译码相比,max-log MAP译码的复杂度大为降低,而译码性能的损失微乎其微。WMLG译码与max-log MAP译码的等价关系表明,基于WMLG译码的混合译码算法都可看作max-log MAP算法的改进,这对于设计LDPC码的新型混合译码算法有较好的指导作用。

A new derivation method of the weighted majority-logic（WMLG） decoding for low-density parity-check（LDPC） codes is proposed based on the maximum-logarithm（max-log） maximum a posteriori（MAP） decoding to illustrate the physical significance of WMLG decoding.The logarithm likelihood ratio（LLR） of information bit is approximated using the logarithm approximation to the sum of powers.Then it is theoretically proved that the WMLG decoding is identical to the max-log MAP decoding.Furthermore,the simulation results show that the max-log MAP decoding has almost the same error performance as the MAP decoding has,while the complexity is greatly reduced.The equivalence between the WMLG decoding and the max-log MAP decoding shows that all WMGL-based hybrid decoding algorithms can be regarded as revised versions of the max-log MAP decoding,which gives a guide to devise new hybrid decoding algorithms of LDPC codes.