Spatially Coupled PLDPC-Hadamard Convolutional Codes

TL;DR

This paper introduces spatially coupled PLDPC-Hadamard convolutional codes that approach the Shannon limit, with an efficient decoding algorithm and threshold estimation method, demonstrating superior error performance over existing codes.

Contribution

It presents a novel class of spatially coupled codes, a combined decoding algorithm, and a systematic approach to optimize code thresholds, advancing near-Shannon-limit coding techniques.

Findings

Codes achieve thresholds close to block code counterparts.

Simulations show superior error performance compared to state-of-the-art codes.

Bit error rate of 1e-5 at -1.465 dB Eb/N0, near Shannon limit.

Abstract

We propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard block codes. We develop an efficient decoding algorithm that combines pipeline decoding and layered scheduling for the decoding of SC-PLDPCH-CCs, and analyze the latency and complexity of the decoder. To estimate the decoding thresholds of SC-PLDPCHCCs, we first propose a layered protograph extrinsic information transfer (PEXIT) algorithm to evaluate the thresholds of spatially coupled PLDPC-Hadamard terminated codes (SC-PLDPCH-TDCs) with a moderate coupling length. With the use of the proposed layered PEXIT method, we develop a genetic algorithm to find good SC-PLDPCH-TDCs in a systematic way. Then we extend the coupling length of these SC-PLDPCH-TDCs to form good SC-PLDPCH-CCs. Results show that our constructed SC-PLDPCH-CCs can achieve comparable thresholds to the block code counterparts. Simulations illustrate the superiority of the SC-PLDPCH-CCs over the block code counterparts and other state-of-the-art low-rate codes in terms of error performance. For the rate-0.00295 SC-PLDPCH-CC, a bit error rate of 1e-5 is achieved at Eb/N0 = -1.465 dB, which is only 0.125 dB from the ultimate Shannon limit.