Obtaining extra coding gain for short codes by block Markov superposition transmission

In this paper, we present a new approach, called block Markov superposition transmission (BMST), to construct from short codes a class of convolutional codes with large constraint length. The BMST is very similar to superposition block Markov encoding (SBME), which has been widely used to prove multiuser coding theorems. We also present an iterative sliding-window decoding algorithm for the proposed transmission scheme. The extra coding gain obtained by BMST can be bounded in terms of the Markov order and with the help of the input-output weight enumerating function (IOWEF) of the BMST system, which can be computed from that of the short code by performing a trellis-based algorithm. Numerical results verify our analysis and show that an extra coding gain of 6.4 dB at bit-error rate (BER) 10^-5 can be obtained by BMST of the [7, 4] Hamming code.