Constructing high-rate scale-free LDPC codes

Low-density parity-check (LDPC) codes with scale-free (SF) symbol-node degree distribution have been shown to provide very good error performance. When the code rate becomes high, however, there will be a lot of degree-2 symbol nodes in the “pure” SF-LDPC codes. As a consequence, when the codes are constructed by connecting the symbol nodes with the check nodes, many small-size cycles will be formed. Such small-cycles will degrade the error performance of the codes. In this paper, we address the issue by imposing a new constraint on the design of high-rate SF-LDPC codes. We will compare the error rates of the constrained SF-LDPC codes and other optimized LDPC codes.