Design of finite-length rate-compatible LDPC codes

This paper considers rate-compatible puncturing for finite-length low-density parity-check (LDPC) codes. Among the existing systematic puncturing methods, the grouping and sorting algorithm (GSA) stands out for its good performance and easy implementation, but as is proven in this paper, there exists a limit on the amount of puncturing that can be done, which restricts the range of the achievable code rates as well as the choice of the mother code. A new puncturing algorithm with better flexibility is developed. The new algorithm can be generally applied to an arbitrary irregular or regular LDPC code to obtain a code rate arbitrarily close to 1, and at the same time to achieve performance that is superior to the GSA.