Determination of Minimal Matrices of Simple Cycles in Ldpc Codes

Simple cycles are the easiest cycles to reveal in Low-Density Parity Check (LDPC) codes. All minimum matrices of simple cycles with the same length will be equivalent after row or column permutations .In this paper,we analysis the structure of simple cycles and show all figures of minimal matrices of simple cycles. Firstly, we introduce a more general definition of cycle and investigate simple cycles in LDPC codes. Secondly, we present the number of simple cycles of arbitrary length and all the minimal matrices of simple cycles. Finally, we have proved that the number of all minimal matrices of 2k-simple cycles is 3 , . 2 )! 1 ( ≥ − k for P k k k .