Block Markov Superposition Transmission: Construction of Big Convolutional Codes from Short Codes

TL;DR

This paper introduces Block Markov Superposition Transmission (BMST), a method to construct large convolutional codes from short codes, offering near-optimal performance with efficient decoding, applicable to both linear and nonlinear codes.

Contribution

The paper proposes BMST as a novel approach to build big convolutional codes from short codes, with a simple performance bound and near-Shannon-limit results.

Findings

BMST with repetition and parity-check codes approaches Shannon limit within 0.5 dB.

Decoding can be performed with an iterative sliding-window algorithm.

Performance bounds are effectively matched with moderate decoding delay.

Abstract

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.