Improving the Decoding Threshold of Tailbiting Spatially Coupled LDPC Codes by Energy Shaping

TL;DR

This paper introduces energy shaping, a method to improve the decoding threshold of tailbiting spatially coupled LDPC codes by varying transmission energies, achieving thresholds close to terminated codes without rate loss.

Contribution

It proposes an energy shaping technique with an optimal boosting policy to enhance decoding thresholds of tailbiting SC-LDPC codes without rate loss.

Findings

Thresholds close to terminated codes achieved

Optimal energy boosting policy derived

Monte Carlo simulations confirm effectiveness

Abstract

We show how the iterative decoding threshold of tailbiting spatially coupled (SC) low-density parity-check (LDPC) code ensembles can be improved over the binary input additive white Gaussian noise channel by allowing the use of different transmission energies for the codeword bits. We refer to the proposed approach as energy shaping. We focus on the special case where the transmission energy of a bit is selected among two values, and where a contiguous portion of the codeword is transmitted with the largest one. Given these constraints, an optimal energy boosting policy is derived by means of protograph extrinsic information transfer analysis. We show that the threshold of tailbiting SC-LDPC code ensembles can be made close to that of terminated code ensembles while avoiding the rate loss (due to termination). The analysis is complemented by Monte Carlo simulations, which confirm the viability of the approach.