  In this paper, we propose a simple procedure to construct (decodable) good
codes with any given alphabet (of moderate size) for any given (rational) code
rate to achieve any given target error performance (of interest) over additive
white Gaussian noise (AWGN) channels. We start with constructing codes over
groups for any given code rates. This can be done in an extremely simple way if
we ignore the error performance requirement for the time being. Actually, this
can be satisfied by repetition (R) codes and uncoded (UN) transmission along
with time-sharing technique. The resulting codes are simply referred to as RUN
codes for convenience. The encoding/decoding algorithms for RUN codes are
almost trivial. In addition, the performance can be easily analyzed. It is not
difficult to imagine that a RUN code usually performs far away from the
corresponding Shannon limit. Fortunately, the performance can be improved as
required by spatially coupling the RUN codes via block Markov superposition
transmission (BMST), resulting in the BMST-RUN codes. Simulation results show
that 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-interleaved
coded modulation (BMST-BICM) scheme.
