On Average Number of Cycles in Finite-Length Spatially Coupled LDPC Codes.

In this paper, a probabilistic analysis of the cycle distribution of protograph-based spatially coupled low-density parity-check (SC LDPC) codes is presented. In particular, we derive the probability that cycles of specific, but arbitrary, length are broken as a result of spatial coupling with a random spreading matrix in a general edge spreading process. Our results show that the probability of existence of cycles in SC codes is O(1/m), where m is the code memory. This result is independent of the cycle length.