Multiple-rate codes from block Markov superposition transmission of first-order Reed-Muller and extended Hamming codes
Block Markov superposition transmission (BMST) of first-order Reed-Muller and extended Hamming (RMEH) codes is investigated. Multiple code rates can be easily realised by adjusting the mixture ratio of Reed-Muller and extended Hamming codes. Compared with the original BMST of repetition and single-parity-check (RSPC) codes, the proposed BMST-RMEH codes can perform close to Shannon limits over a wide range of code rates with about only half the encoding memories of BMST-RSPC codes. As a result of the reduction of encoding memories, the decoding complexity and delay of BMST-RMEH codes are approximately half (or even lower than) those of BMST-RSPC codes.