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STRUCTURE, PROPERTY, AND DESIGN OF NONBINARY REGULAR CYCLE CODES

ABSTRACT 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. INDEX TERMS LDPC, regular cycle code, Galois field, graph theory, decoding algorithm, code design

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