A New Simulation Approach to Performance Evaluation of Binary Linear Codes in the Extremely Low Error Rate Region

TL;DR

This paper introduces a novel simulation method for evaluating binary linear codes' performance in extremely low error rate regions, leveraging a new interpretation of the sphere bound that decouples code geometry from noise statistics.

Contribution

It proposes a new simulation approach based on nested Gallager regions, enabling efficient performance evaluation in low error rate regimes.

Findings

The approach matches traditional methods at high error rates.

It efficiently evaluates performance in extremely low error rate regions.

The method decouples code geometry from noise statistics.

Abstract

In this paper, the sphere bound (SB) is revisited within a general bounding framework based on nested Gallager regions. The equivalence is revealed between the SB proposed by Herzberg and Poltyrev and the SB proposed by Kasami et al., whereas the latter was rarely cited in the literatures. Interestingly and importantly, the derivation of the SB based on nested Gallager regions suggests us a new simulation approach to performance evaluation of binary linear codes over additive white Gaussian noise (AWGN) channels. In order for the performance evaluation, the proposed approach decouples the geometrical structure of the code from the noise statistics. The former specifies the conditional error probabilities, which are independent of signal-to-noise ratios (SNRs) and can be simulated and estimated efficiently, while the latter determines the probabilities of those conditions, which involve SNRs and can be calculated numerically. Numerical results show that the proposed simulation approach matches well with the traditional simulation approach in the high error rate region but is able to evaluate efficiently the performance in the extremely low error rate region.