Cycle analysis of time-variant LDPC convolutional codes

Time-variant Low-Density Parity-Check convolutional codes (LDPCccs) can be derived from unwrapping Quasi-Cyclic (QC) LDPC block codes. Rather than analyzing cycles in a large-scale time-domain parity check matrix, we propose a new way to describe cycle properties in compact form by a “polynomial syndrome former”, i.e., a syndrome former in an equivalent polynomial representation. According to the relationship of cycle structures between time- and polynomial-domain syndrome formers, we present a cycle counter algorithm to analyze cycle properties in time-variant LDPCccs as well as in time-invariant LDPCccs.