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

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 block Markov encoding (SBME), which has been widely used to prove multiuser coding theorems. The BMST codes can also be viewed as a class of spatially coupled codes, where the generator matrices of the involved short codes (referred to as basic codes) are coupled. The encoding process of BMST can be as fast as that of the basic 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 sliding-window 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 the BER of 10 −5 for a wide range of code rates; and 3) BMST can also be applied to nonlinear codes.

Capacity Bound and Ber Performance of Ofdm System in High-Mobility Scenarios

“…The encoding process with memory m is described in [16]. As for the decoding algorithm, we take the sliding-window decoding into account in the BMST-OFDM system.…”

Block Markov superposition transmission with pulse position modulation over free-space optical links

“…BMST (Block Markov Superposition Transmission) is a recently proposed coding scheme [27] . In the BMST scheme, binary sequences are encoded with a basic code and then transmitted multiple times (in their interleaved versions) to improve the transmission reliability.…”

“…Meanwhile, the interleaved sequences are superimposed in a block Markov manner to maintain the transmission efficiency. Any short code (linear or nonlinear) with a fast encoding algorithm and an efficient SISO (Soft-In SoftOut) decoding algorithm can be chosen as the basic code [27] . BMST also has a simple but tight performance lower bound.…”

“…BMST also has a simple but tight performance lower bound. Furthermore, BMST is effective in constructing capacity-approaching coding schemes for AWGN (Additive White Gaussian Noise) channels [27] . However, its combination with PPM over FSO links has never been investigated in the literature.…”

A Joint Algorithm of Equalizer and Detector Based on Coded-Ofdm Systems in High-Speed Channels

“…In recent years, a coded scheme called block Markov superposition transmission (BMST) codes was proposed [11], whose performance can be predicted by a simple genie-aided bound. In addition, the design of BMST codes is flexible in the sense that any code of any rate with fast encoding algorithm and efficient SISO decoding algorithm can be taken as the basic code.…”