Stability analysis of an improved min-sum decoder

It has been shown that under min-sum (MS) decoding, scaling the messages at the output of check nodes can improve the performance of regular low-density parity-check (LDPC) codes. However, for irregular codes designed for the sum-product decoder, linear scaling can hinder the performance. The problem of code design for MS and linear scaling min-sum (LSMS) decoders have been recently investigated. It is shown that the gap to the capacity for LSMS codes is better than MS codes, but compared to sum-product codes the gap is still considerable. In this letter, a modified MS decoding is proposed and studied. We use the stability analysis of density evolution to show that the proposed method allows for a larger fraction of edges connected to degree-2 variable nodes than LSMS codes. Finally, by designing codes based on the modified method, we show that compared to MS and LSMS codes, a smaller gap to the capacity can indeed be achieved while the complexity of decoding remains essentially the same.