Low Rate Concatenated Zigzag-Hadamard Codes

We introduce a new class of low-rate error correction codes called concatenated zigzag Hadamard (ZH) codes which are specified by a highly structured zigzag graph with each segment being a Hadamard codeword. The ZH codes enjoy extremely simple encoding and very-low-complexity soft-input soft-output (SISO) decoding. We present an asymptotic performance analysis of the proposed codes using the extrinsic mutual information transfer (EXIT) chart for infinite-length codes. We also provide a union bound analysis of the error performance for finite-length codes.