Near Shannon limit precoded concatenated zigzag codes

Concatenated zigzag (CZ) codes are a class of multidimensional parallel concatenated codes, which have some favorable properties, such as low encoding and decoding complexities and rate compatibility. However, there is a noticeable gap between the performance of a standard CZ code and the corresponding Shannon limit. To overcome this problem, we apply the precoding technique recently developed by Abbasfar et al. to CZ codes, resulting in a novel class of turbo-like codes, termed precoded CZ codes. The EXIT chart tool is used for convergence analysis and performance optimization. We show that the proposed precoded CZ codes have thresholds within 0.25 dB of the Shannon limit for a wide code rate range of [0.5, 20/21]. Extensive simulation results are provided to demonstrate that optimized precoded CZ codes exhibit good performance at different code rates and different block lengths.