Spatially Coupled Codes and Optical Fiber Communications: An Ideal Match?

In this paper, we highlight the class of spatially coupled codes and discuss their applicability to long-haul and submarine optical communication systems. We first demonstrate how to optimize irregular spatially coupled LDPC codes for their use in optical communications with limited decoding hardware complexity and then present simulation results with an FPGA-based decoder where we show that very low error rates can be achieved and that conventional block-based LDPC codes can be outperformed. In the second part of the paper, we focus on the combination of spatially coupled LDPC codes with different demodulators and detectors, important for future systems with adaptive modulation and for varying channel characteristics. We demonstrate that SC codes can be employed as universal, channel-agnostic coding schemes.Comment: Invited paper to be presented in the special session on "Signal Processing, Coding, and Information Theory for Optical Communications" at IEEE SPAWC 201

A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially-coupled ensembles when transmission takes place over the binary erasure channel. We discuss how the parameters of the scaling law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the scaling law fit well to the data derived from simulations over a wide range of parameters. The ultimate goal of this line of research is to develop analytic tools for the design of spatially-coupled LDPC codes under practical constraints

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

Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding

A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially-coupled GLDPC codes with BCH component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution (DE).Comment: 22 pages, this version accepted to the IEEE Transactions on Information Theor