Application of complex-network theories to the design of short-length low-density-paritycheck codes

Study of complex networks has been conducted across many fields of science, including computer networks, biological networks and social networks. Characteristics of different types of complex networks such as random networks, regular-coupled networks, small-world networks and scale-free networks have been discovered by researchers. Application of such network properties to solve engineering problems, however, is still at the infancy stage. In this study, we make one of the first attempts in applying complex network theories to communications engineering. In particular, inspired by the shortest-average-path-length property of scale-free networks, we design short-length low-density-parity-check (LDPC) codes with an aim to shortening the average distance between any two variable nodes. We will also compare the error performance, both theoretically and by simulations, of the proposed codes with those of other well-known LDPC codes.