Improved Weighted Bit Flip Voting decoding algorithm for generalized LDPC

Abstract

A generalized low-density parity-check code (GLDPC) is a low-density parity-check code in which the constraint nodes of the code's graph are replaced with a small linear block code referred to as the constituent code other than single parity checks. For the optical system or ultra-high speed wireless data transfer system, it is hard to gain soft LLRs which need to be supplied by ultra-high speed A/D converters, so the hard decision decoder is important for these systems. Similar with Gallager's bit-flipping algorithm for LDPC, the Weighted Bit Flip Voting (WBFV) algorithm has been proposed to decode GLDPC with only the hard decision which proved to be good performance. But the finding of max vote in the algorithm is intractability for the hardware implementation. If we find the max from thousands of data (code length is usually thousands) serially, thousands of cycles needed result to large latency; a lot of compare modules needed for parallel finding of the max, result to large resource. In this paper, we proposed an improved and simplified WBFV algorithm which without max voting finding is easy for hardware implementation. The proposed improved algorithm not only has no performance loss, but also speeds up the iteration convergence. Then we proposed a full parallel GLDPC decoder design for our algorithm with very low complexity.