1New Codes on Graphs Constructed by Connecting Spatially Coupled Chains
Dmitri V. Truhachev, David G. M. Mitchell, Michael Lentmaier, Senior Member, Daniel J. Costello, Life Fellow · 2016
A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual SC-LDPC codes. We demonstrate that code ensembles obtained by connecting appropriately chosen SC-LDPC code chains at specific points have improved iterative decoding thresholds compared to those of single SC-LDPC coupled chains. In addition, it is shown that the improved decoding properties of the connected ensembles result in reduced decoding complexity required to achieve a specific bit error probability. The constructed ensembles are also asymptotically good, in the sense that the minimum distance grows linearly with the block length. Finally, we show that the improved asymptotic properties of the connected chain ensembles also translate into improved finite length performance. Index Terms Spatial graph coupling, spatially coupled codes, connected chain ensembles, protographs, LDPC convolutional codes, iterative decoding.