Protograph E²RC Codes

We propose a construction of rate-compatible punctured codes based on protographs that have a special E²RC structure in their parity part (E²RC codes were introduced in Kim, Ramamoorthy and McLaughlin ´06) . The protograph representation of these codes facilitates their asymptotic performance analysis and allows the implementation of high speed decoders. The construction process starts with a good high rate protograph. The protographs of lower rate codes are derived from the higher rate protographs via the process of check-splitting. The check-splitting is done in a specific manner so that the parity nodes in the protograph have the special E²RC structure. We also present additional design rules that ensure that the gap to capacity remains low across the range of rates. Using our approach we exhibit protographs that have a gap of at most 0.27 dB to capacity across the range of rates 1/2 to 8/9. These conclusions are supported by our simulation results. Our work, therefore presents a systematic method for the design of E²RC-like codes.