Spatially Coupled LDPC Codes Constructed from Protographs
David G. M. Mitchell, Michael Lentmaier, and Daniel J. Costello Jr

TL;DR
This paper introduces a flexible family of spatially coupled LDPC codes from protographs that achieve near-capacity thresholds with efficient decoding, combining features of regular and irregular codes for various rates and lengths.
Contribution
The paper presents a novel construction of protograph-based spatially coupled LDPC codes that attain capacity-approaching thresholds and exhibit linear minimum distance growth, with scalable architectures.
Findings
BP thresholds approach MAP thresholds for large L
Error probability converges doubly exponentially with iterations
Codes can achieve capacity with low-complexity BP decoding
Abstract
In this paper, we construct protograph-based spatially coupled low-density parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary L. We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large L, the BP thresholds on both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise channel (AWGNC) saturate to a particular value significantly better than the BP decoding…
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