Structure, property, and design of nonbinary regular cycle codes

In this paper, we study nonbinary regular LDPC cycle codes whose parity check matrix H has fixed column weight j = 2 and fixed row weight d. Through graph analysis, we show that the parity check matrix H of a regular cycle code can be put into an equivalent structure in the form of concatenation of row-permuted block-diagonal matrices 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. This equivalent structure of H enables: i) parallel processing in lineartime encoding; ii) considerable resource reduction on the code storage for encoding and decoding; and iii) parallel processing in sequential belief-propagation decoding, which increases the throughput without compromising performance or complexity. On the code´s structure design, we propose a novel design methodology based on the equivalent structure of H. Finally, we present various numerical results on the code performance and the decoding complexity.