On the asymptotic performance of spatially-coupled codes with minimal coupling

Spatially-coupled codes have low-complexity structures and a low-delay decoding architecture, which nominate them as a very desirable candidate for communication standards. In this paper, a study on the asymptotic performance of spatially-coupled ensembles over the binary erasure channel (BEC) with density evolution analysis based on the belief-propagation algorithm is conducted. We identify all possible members of base matrices with minimal coupling (corresponding to a code memory of one and two) for asymptotically (3; 6)-regular spatially-coupled codes. For ensembles with single memory, block decoding and window decoding thresholds are calculated and for ensembles with memory of two, window decoding thresholds are calculated. It is shown that not only block decoding thresholds of finite-length spatially-coupled ensembles over BEC is better than LDPC block codes, but also are their window decoding thresholds. Based on the results, spatially-coupled code ensembles with the best performance are identified and some practical code design criteria are presented.