Spatial Coupling of Generator Matrix: A General Approach to Design of Good Codes at a Target BER

TL;DR

This paper introduces a systematic design methodology for spatially coupled generator matrices in BMST systems, enabling near-capacity performance at very low BERs by using a two-phase decoding approach and performance bounds.

Contribution

It proposes a general approach to design BMST codes with predictable performance close to Shannon capacity at targeted BERs, using a novel two-phase decoding and genie-aided bounds.

Findings

Achieves performance within 1 dB of Shannon limit at BER of 10^-15

Uses Cartesian product of short codes for simplified design

Demonstrates effective two-phase decoding with performance prediction

Abstract

For any given short code (referred to as the basic code), block Markov superposition transmission (BMST) provides a simple way to obtain predictable extra coding gain by spatial coupling the generator matrix of the basic code. This paper presents a systematic design methodology for BMST systems to approach the channel capacity at any given target bit-error-rate (BER) of interest. To simplify the design, we choose the basic code as the Cartesian product of a short block code. The encoding memory is then inferred from the genie-aided lower bound according to the performance gap of the short block code to the corresponding Shannon limit at the target BER. In addition to the sliding-window decoding algorithm, we propose to perform one more phase decoding to remove residual (rare) errors. A new technique that assumes a noisy genie is proposed to upper bound the performance. Under some mild assumptions, these genie-aided bounds can be used to predict the performance of the proposed two-phase decoding algorithm in the extremely low BER region. Using the Cartesian product of a repetition code as the basic code, we construct a BMST system with an encoding memory 30 whose performance at the BER of $10^{-15}$ can be predicted within one dB away from the Shannon limit over the binary-input additive white Gaussian noise channel (BI-AWGNC).