A comparison between the sum-product and the min-sum iterative detection algorithms based on density evolution

Recently, density evolution techniques have been used to predict the performance of iterative decoders utilizing the sum-product belief propagation algorithm. We extend this analysis to the min-sum algorithm for binary codes. Using two representative applications, i.e., low-density parity-check (LDPC) codes and repeat accumulate (RA) codes, the sum-product and min-sum algorithms are compared. The results demonstrate a performance degradation of 0.27-1.03 dB for the min-sum algorithm, which confirms earlier simulation results. However, it is shown that a small modification to the min-sum algorithm results in an approximate sum-product algorithm, which performs at least as well as the original sum-product algorithm when finite message precision is considered