Abstract: An efficient implementation of the sum-product algorithm(SPA) in the log-likelihood ratio(LLR) domain is presented in [1]. In this paper, we modify a formula in [1] such that SPA can be implemented by using two small look-up tables. With this modification, all the calculations involved in this implementation involve only additions, subtractions, comparisons and table looking-ups, which leads to low computation complexity and facility in hardware implementation. Based on this modified implementation, various quantization schemes of SPA for decoding low-density parity-check(LDPC) codes are investigated. And the issues related to quantization, such as clipping levels and variables' quantization, are also investigated. Simulation results show that the performance of the uniform quantization scheme is very close to that of the non-quantization over the AWGN channel. Moreover, it can obtain the same performance as that of non-quantization at high SNRs.

Key words: sum-product algorithm, iterative decoding, forward/backward algorithm, parallel implementation, LDPC codes