Zigzag codes and concatenated zigzag codes

This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in, soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-MAP (MLM) formulation, which requires a total of only 20 addition-equivalent-operations per information bit, per iteration. Simulation of a rate-1/2, four-dimensional concatenated zigzag code with interleaver length 65536 yields a bit error rate (BER) of 10^-5 at 0.9 dB and 1.4 dB away from the Shannon theoretical limit by optimal (MAP) and low-cost sub-optimal (MLM) decoders, respectively. Furthermore, these codes appear to have lower error floors than the comparable two-dimensional turbo codes