Protograph-based Raptor-like LDPC codes for the binary erasure channel

This paper designs protograph-based Raptor-like (PBRL) codes as a class of rate-compatible (RC) LDPC codes for binary-erasure channels (BEC). Similar to the Raptor Codes, the RC property is achieved by X-OR operations of the precoded bits. The additional parity bits, which lower the rate, are selected such that their connections in the protograph optimize the density evolution threshold. In order to avoid problematic graphical objects in the CPEG lifted bipartite graph and guarantee the linear growth distance property some constraints are imposed in the threshold optimization algorithm. Simulation results are presented for information block sizes of k = 1032, and k = 16384. These results are compared with finite blocklength bounds of Polyanskiy, Poor, Verdu (PPV) as well as several asymptotic bounds. The k = 1032 code family operates at various rates in the range of 8/9 to 8/48 and has an average normalized threshold gap of 5.56% from capacity. The k = 16384 code family operates at rates 8/10 to 8/32 and has an average normalized threshold gap of 3.27% from capacity.