期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 67, 期 4, 页码 2217-2235出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2021.3059414
关键词
Parity check codes; Error analysis; Convolutional codes; Decoding; Block codes; Sparse matrices; Upper bound; Convolutional codes; girth; LDPC codes; spatially coupled codes; time-invariant codes; time-varying codes
This paper demonstrates that the limitations of time-invariant SC-LDPC codes can be overcome by transforming them into time-varying SC-LDPC codes with small period. The research shows that periodically time-varying SC-LDPC codes with small period may exhibit significantly better girth properties than the corresponding time-invariant codes by utilizing a larger number of degrees of freedom in the code design.
Time-varying spatially coupled low-density parity-check (SC-LDPC) codes with very large period are characterized by significantly better error rate performance and girth properties than their time-invariant counterparts, but the number of parameters they require to be described is usually very large and unpractical. Time-invariant SC-LDPC codes, which can be seen as periodically time-varying codes with unitary period, are represented through a small number of parameters and designed exploiting few degrees of freedom, but their error rate performance and girth properties are sub-optimal. In this paper, we show that the limits of time-invariant SC-LDPC codes can be overcome by transforming them into time-varying SC-LDPC codes with very small period. In particular, we show that periodically time-varying SC-LDPC codes with small period may exhibit significantly better girth properties than the corresponding time-invariant codes by exploiting a larger number of degrees of freedom in the code design, which however scale at most linearly with the product of the code period and the size of the considered base matrix.
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