Structure of non-binary regular ldpc cycle codes

In this paper, we study non-binary regular LDPC cycle codes whose parity check matrix has fixed column weight 2 and fixed row weight d. We prove that the parity check matrix of any regular cycle code can be put into a concatenation form of row-permuted block-diagonal matrices after row and column permutations if d is even, or, if d is odd and the code's associated graph contains at least one spanning subgraph that consists of disjoint edges. Utilizing this structure enables parallel processing in linear-time encoding, and parallel processing in sequential belief-propagation decoding, which increases the throughput without compromising performance or complexity. Numerical results are presented to compare the code performance and the decoding complexity.