Spatially Coupled PLDPC-Hadamard Convolutional Codes

Abstract

In this paper, 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 also develop an efficient decoding algorithm that combines pipeline decoding and layered scheduling for the decoding of SC-PLDPCH-CCs. To estimate the decoding thresholds of SC-PLDPCH-CCs, 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 look for good SC-PLDPCH-TDCs in a systematic way. Subsequently, we extend the coupling length of these SC-PLDPCH-TDCs with good thresholds to form good SC-PLDPCH-CCs. Based on the same set of split protomatrices, we regard the threshold of SC-PLDPCH-TDC as the proxy of SC-PLDPCH-CC when the SC-PLDPCH-TDC with long coupling length has almost the same code rate as the SC-PLDPCH-CC.Results show that our optimized SC-PLDPCH-CCs can achieve comparable thresholds to the block code counterparts. Simulations also illustrate the superiority of the SC-PLDPCH-CCs over the block code counterparts in terms of error performance. Moreover, for the rate-0.00295 SC-PLDPCH-CC, a BER of 10 −7 is achieved at E b /N 0 = −1.45 dB, which is only 0.14 dB from the ultimate Shannon limit.