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

Analysis and Design of Partially Information- and Partially Parity-Coupled Turbo Codes

In this paper, we study a class of spatially coupled turbo codes, namely partially information- and partially parity-coupled turbo codes. This class of codes enjoy several advantages such as flexible code rate adjustment by varying the coupling ratio and the encoding and decoding architectures of the underlying component codes can remain unchanged. For this work, we first provide the construction methods for partially coupled turbo codes with coupling memory $m$ and study the corresponding graph models. We then derive the density evolution equations for the corresponding ensembles on the binary erasure channel to precisely compute their iterative decoding thresholds. Rate-compatible designs and their decoding thresholds are also provided, where the coupling and puncturing ratios are jointly optimized to achieve the largest decoding threshold for a given target code rate. Our results show that for a wide range of code rates, the proposed codes attain close-to-capacity performance and the decoding performance improves with increasing the coupling memory. In particular, the proposed partially parity-coupled turbo codes have thresholds within 0.0002 of the BEC capacity for rates ranging from $1/3$ to $9/10$, yielding an attractive way for constructing rate-compatible capacity-approaching channel codes.Comment: 15 pages, 13 figures. Accepted for publication in IEEE Transactions on Communication