Zigzag codes and concatenated zigzag codes

This paper introduces a family of error-correcting codes called zigzag code s, A zigzag code is described by a highly structured zigzag graph, Due to t he structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on th e Max-Log-APP (MLA) formulation, which requires a total of only 20 addition -equivalent operations per information bit, per iteration. Simulation of a rate-1/2 concatenated zigzag code with four constituent encoders with inter leaver length 65 536, yields a bit error rate (BER) of 10(-5) at 0.9 dB and 1.4 dB away from the Shannon limit by optimal (APP) and low-cost suboptima l (MLA) decoders, respectively. A union bound analysis of the bit error pro bability of the zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also illustrated that, for a fixed interleaver size, the concatenated code has increased cod e potential as the number of constituent encoders increases. Finally, the a nalysis shows that zigzag codes with four or more constituent encoders have lower error floors than comparable turbo codes with two constituent encode rs.