  A construction of big convolutional codes from short codes called block
Markov superposition transmission (BMST) is proposed. The BMST is very similar
to superposition blockMarkov encoding (SBME), which has been widely used to
prove multiuser coding theorems. The encoding process of BMST can be as fast as
that of the involved short code, while the decoding process can be implemented
as an iterative sliding-window decoding algorithm with a tunable delay. More
importantly, the performance of BMST can be simply lower-bounded in terms of
the transmission memory given that the performance of the short code is
available. Numerical results show that, 1) the lower bounds can be matched with
a moderate decoding delay in the low bit-error-rate (BER) region, implying that
the iterative slidingwindow decoding algorithm is near optimal; 2) BMST with
repetition codes and single parity-check codes can approach the Shannon limit
within 0.5 dB at BER of 10^{-5} for a wide range of code rates; and 3) BMST can
also be applied to nonlinear codes.
