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In this paper, we propose a simple procedure to construct (decodable) goodcodes with any given alphabet (of moderate size) for any given (rational) coderate to achieve any given target error performance (of interest) over additivewhite Gaussian noise (AWGN) channels. We start with constructing codes overgroups for any given code rates. This can be done in an extremely simple way ifwe ignore the error performance requirement for the time being. Actually, thiscan be satisfied by repetition (R) codes and uncoded (UN) transmission alongwith time-sharing technique. The resulting codes are simply referred to as RUNcodes for convenience. The encoding/decoding algorithms for RUN codes arealmost trivial. In addition, the performance can be easily analyzed. It is notdifficult to imagine that a RUN code usually performs far away from thecorresponding Shannon limit. Fortunately, the performance can be improved asrequired by spatially coupling the RUN codes via block Markov superpositiontransmission (BMST), resulting in the BMST-RUN codes. Simulation results showthat the BMST-RUN codes perform well (within one dB away from Shannon limits)for a wide range of code rates and outperform the BMST with bit-interleavedcoded modulation (BMST-BICM) scheme.

Block Markov Superposition Transmission of RUN Codes