Can cyclic codes be useful low-density parity-check codes?

Traditionally, low-density parity-check (LDPC) codes are constructed randomly and it is not clear whether algebraically constructed codes, such as cyclic codes, can compete with the error correction performances of the random codes. We consider in this paper new cyclic low-density parity-check codes decoded with the sum-product algorithm. The cyclic codes we present have sparse parity-check matrices, good minimum distance and girth 6. Using frnite-length analysis and simulation results we show that the most significant benefit of the new codes, in terms of error correction performance, is the linearly dependent rows in their parity-check matrices. Our results suggest that increasing column weight to improve the minimum distance and the minimum stopping set size of the code proves beneficial at low erasure probabilities but adversely affects performance in channels with high erasure probabilities.