On the performance of fixed-length spatially coupled LDPC code

This paper evaluates the rate loss of fixed-length spatially-coupled low-density parity-check (SC-LDPC) code compared to the asymptotic performance of such code. In previous works, SC-LDPC with sufficient length of codeword shows excellent asymptotic performance and attracts a lot of attentions. However, when the length of codeword is limited, the performance of SC-LDPC code with limited codeword-length is not as well studied as its counterpart with infinite codeword-length. In this paper, the rate loss of a fixed-length SC-LDPC will be analyzed from two aspects: the rate loss due to finite length of the uncoupled code, and the rate loss due to finite length of the coupling chain. Furthermore, through trade-off between the length of the coupling chain and that of the uncoupled code, the rate loss of the SC-LDPC is optimized. The optimization results show that the trend of the rate loss of a length-N SC-LDPC is O(N-1/3) and is different from that of a conventional LDPC code [1], which is O(N-1/2). In other words, for achieving similar performance of a conventional length-N LDPC code, the length of an SC-LDPC code should be increased to O(N3/2).