基于置信传播算法的低密度校验码量化译码设计

介绍了二元输入连续输出无记忆AWGN信道下低密度校验 (LDPC)码的置信传播译码算法及其密度进化特性 .根据密度进化规律 ,分析了不同消息空间中的量化译码问题 .得出结论如下 :对于概率和概率差消息 ,只有高阶均匀量化才能获得满意的译码性能 ;似然比消息的适当对数量化可等价于对数似然比消息的均匀量化 ;对数似然比消息易于实现相对信道输入± 1的无偏对称量化 ,并有效利用消息的统计特性 .由非均匀量化在大消息区域分配的量化电平可以有效地促进算法收敛 .仿真结果表明 ,低阶非均匀量化优于均匀量化

Quantized Decoding of LDPC Codes with Belief Propagation Algorithm

The belief propagation algorithm for decoding low-density parity-check (LDPC) codes in the binary-input continuous-output memoryless AWGN channel is introduced. According to the behaviors of density evolution,the existing problems on quantization design for iterative decoding in different message spaces are discussed. Since messages in the form of probability or probability difference present opposite gathering tendencies with respect to channel inputs 1 and -1 in density evolution as iteration grows,the only proper selection for the time-invariant quantized decoding is then uniform quantization which generally needs more quantization bits to achieve a satisfactory performance. In contrary,the log-likelihood ratio messages roughly have the Gaussian mixture densities during iterations,this makes it simple to perform symmetric quantization and hence to provide unbiased measures for coded bits 1 and -1 at the channel input such that the error performance of quantized decoding is independent of the transmitted codeword. Nonuniform quantization can share the Gaussian characteristics in order to approach non-quantized decoding. Furthermore,when using nonuniform quantization,some levels can be allocated across the larger message region,which may improve the convergence of belief propagation in case the algorithm is convergent,and this makes the nonuniform scheme outperform the uniform one. This is true especially for quantization of very low resolution. Simulations demonstrate an improvement of 0.2dB in terms of coding gains within a region of signal-to-noise ratios with 6-bit logarithmic quantization for a specified regular code of short length. However,the logarithmic quantization with original parameters successful in speech coding is not necessarily applicable in iterative quantized decoding because the messages in decoding have dynamical and different probability density functions during iterations. Thus,the search for optimal quantization parameters is needed to incorporate discretized density evolution,and is left for further work. What we investigate in this paper may be helpful to the implementation of the belief propagation algorithm for decoding LDPC code or other related applications in software or hardware at low cost.