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IEEE Globecom Workshops (GC Wkshps)

Design of Protograph-Based Partial Spatially Coupled LDPC Codes for Windowed Decoding

Inayat Ali, Bonghoe Kim, Dong Sun Lee, Jaehoon Chung

Published Dec 8, 2025• 0 citations
Publisher
DOI
10.1109/gcwkshps68340.2025.11590900

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Spatially coupled low-density parity-check (SC-LDPC) codes are sparse graph codes that have recently become of interest due to their capacity-approaching performance on memoryless binary input channels. Moreover, protograph SC-LDPC codes have been shown to be asymptotically good under certain conditions. SC-LDPC codes are amenable to a windowed decoder that allows decoding of blocks of bits to be done serially, making them good candidates for applications such as streaming. Depending on how they are constructed, however, the codes may still be prone to error floors. One key element in protograph SC-LDPC code design is the edge-spreading method used to couple copies of the base protograph in the construction of the SC-protograph. In this paper, we present an edge-spreading algorithm that is designed to remove trapping sets from the resulting SC-protograph that are harmful with respect to the windowed decoder, and we examine how to determine which trapping sets should be removed in the construction.

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IEEE Transactions on Communications•Jun 9, 2020•28 citations
Spatially coupled (SC) low-density parity-check (LDPC) codes can achieve capacity approaching performance with low message recovery latency when using sliding window (SW) decoding. An SC-LDPC code constructed from a protograph can be generated by first coupling a chain of block protographs and then lifting the coupled protograph using permutation matrices. This paper introduces a systematic design of SC-LDPC codes to eliminate 4-cycles in the coupled photograph. Using a quasi-cyclic (QC) lifting, we obtain QC-SC-LDPC codes of girth at least eight. Coupling a chain of block protographs implies spreading edges from one protograph to the others. Our protograph-based design can be viewed as guiding the edge spreading and also the graph-lifting process. Simulation results show the design leads to improved decoding performance, particularly in the error floor, compared to random designs.
Spatially coupled low-density parity-check (SC-LDPC) codes are sparse graph codes that have recently become of interest due to their capacity-approaching performance on memoryless binary input channels. Moreover, protograph SC-LDPC codes have been shown to be asymptotically good under certain conditions. SC-LDPC codes are amenable to a windowed decoder that allows decoding of blocks of bits to be done serially, making them good candidates for applications such as streaming. Depending on how they are constructed, however, the codes may still be prone to error floors. One key element in protograph SC-LDPC code design is the edge-spreading method used to couple copies of the base protograph in the construction of the SC-protograph. In this paper, we present an edge-spreading algorithm that is designed to remove trapping sets from the resulting SC-protograph that are harmful with respect to the windowed decoder, and we examine how to determine which trapping sets should be removed in the construction.
Spatially coupled (SC) low-density parity-check (LDPC) codes can achieve capacity approaching performance with low message recovery latency when using sliding window (SW) decoding. An SC-LDPC code constructed from a protograph can be generated by first coupling a chain of block protographs and then lifting the coupled protograph using permutation matrices. In this paper, we introduce a systematic design to eliminate 4-cycles in a coupled protograph. Further using a quasi-cyclic (QC) lifting, we introduce a procedure for constructing QC-SC-LDPC codes of girth at least eight. This can be interpreted as a multi-stage graph lifting process that yields a greater flexibility in designing QC-SC-LDPC codes with a large girth than previous approaches. Simulation results show the design leads to improved decoding performance, particularly in the error floor, compared to random constructions. Finally, we determine the minimum coupling width required to eliminate 4-cycles in a coupled protograph.