Overlapped Circular SC-LDPC Codes and Their Modified Coupled Codes

In this paper, overlapped circular spatially-coupled low-density parity-check codes (OC-LDPC) are proposed and their modified coupled codes are derived, which show better performance compared with the spatially-coupled low-density parity-check (SC-LDPC) codes. It is known that the SC-LDPC codes show asymptotically good performance when the chain length is sufficiently large. However, a large chain length requires a large number of decoding iterations, which is often ignored in asymptotic analysis but causes large decoding complexity. The proposed OC-LDPC codes reduce the decoding complexity while maintaining good asymptotic properties of the SC-LDPC codes. The improvement in the decoding complexity comes from that the proposed codes are effectively split into two separate SC-LDPC codes with shorter chain length during decoding process. Thus, the OC-LDPC codes can be decoded with smaller number of decoding iterations. Also, finite-length protograph-based OC-LDPC codes are designed and it is shown that the proposed codes have superior finite-length code performances than the SC-LDPC codes.