Design of 4-cycles Free Short-length LDPC Codes Based on the Kirkman Triple Systems

Short-length codes may play a crucial role in delay-sensitive scenarios. Low-density parity-check (LDPC) codes, as a class of Shannon limit approaching codes, perform well with long code length. However, the design of short-length LDPC codes with good performance is still challenging. This paper investigates the construction of short-length LDPC codes based on the combinatorial design theory. Specifically, Kirkman triple systems (KTS), as a type of balanced incomplete block design (BIBD) techniques, are used to construct the parity-check matrices of LDPC codes, which are guaranteed to be 4-cycles free. Some other properties of such designed LDPC codes are also investigated. For instance, a lower bound on the girth, the code rate and minimum code distance. The simulation results show that the designed short-length LDPC codes based on KTS outperform that of randomly constructed ones.