New Codes on Graphs Constructed by Connecting Spatially Coupled Chains

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.Comment: Submitted to IEEE Transactions on Information Theor

Continuous Transmission of Spatially Coupled LDPC Code Chains

We propose a novel encoding/transmission scheme called continuous chain (CC) transmission that is able to improve the finite-length performance of a system using spatially coupled low-density parity-check (SC-LDPC) codes. In CC transmission, instead of transmitting a sequence of independent code words from a terminated SC-LDPC code chain, we connect multiple chains in a layered format, where encoding, transmission, and decoding are performed in a continuous fashion. The connections between chains are created at specific points, chosen to improve the finite-length performance of the code structure under iterative decoding. We describe the design of CC schemes for different SC-LDPC code ensembles constructed from protographs: a (J,K) -regular SC-LDPC code chain, a spatially coupled repeat-accumulate (SC-RA) code, and a spatially coupled accumulate-repeat-jagged-accumulate (SC-ARJA) code. In all cases, significant performance improvements are reported and it is shown that using CC transmission only requires a small increase in decoding complexity and decoding delay with respect to a system employing a single SC-LDPC code chain for transmission.This material is based upon work supported in part by the National Science Foundation under Grant Nos. CCF-1161754 and CCSS-1710920, in part by NSERC Canada, and in part by the Spanish Ministry of Economy and Competitiveness and the Spanish National Research Agency under grants TEC2016-78434-C3-3-R (AEI/FEDER, EU) and Juan de la Cierva Fellowship IJCI-2014-19150