Error correction in interference-limited wireless systems

TL;DR

A hybrid error and erasure correcting decoder that corrects errors via ORBGRAND and corrects erasures via Gaussian elimination is introduced, which outperform decoding assuming that the LLRs originated from Gaussian noise.

Abstract

We introduce a novel approach to error correction decoding in the presence of additive alpha-stable noise, which serves as a model of interference-limited wireless systems. In the absence of modifications to decoding algorithms, treating alpha-stable distributions as Gaussian results in significant performance loss. Building on Guessing Random Additive Noise Decoding (GRAND), we consider two approaches. The first accounts for alpha-stable noise in the evaluation of log-likelihood ratios (LLRs) that serve as input to Ordered Reliability Bits GRAND (ORBGRAND). The second builds on an ORBGRAND variant that was originally designed to account for jamming that treats outlying LLRs as erasures. This results in a hybrid error and erasure correcting decoder that corrects errors via ORBGRAND and corrects erasures via Gaussian elimination. The block error rate (BLER) performance of both approaches are similar. Both outperform decoding assuming that the LLRs originated from Gaussian noise by 2 to 3 dB for [128,112] 5G NR CA-Polar and CRC codes.

Figures (5)

• Figure 1: Numerically computed LLR values and analytical approximation from 6809154, obtained for $\alpha = 1.5$ and $\gamma = 0.5$.
• Figure 2: Sensitivity analysis of ORBGRAND-EDGE with respect to the threshold $\delta$.
• Figure 3: Performance obtained for a [63,57] CRC code.
• Figure 4: Performance obtained for a [128,116] CA-Polar code.
• Figure 5: Rank ordered LLR values associated to the bits of a codeword affected by Gaussian noise (continuous red line) and by $\alpha$-stable noise (continuous blue line). These result have been generated for a BPSK constellation, a block of size 128, a symmetric alpha stable noise of parameters $(\alpha,\gamma) = (1,0.05)$, and a Gaussian noise of equivalent SNR. Approximations of these reliabilities obtained by means of OBRGRAND and its multiple line variants are represented in dashed lines.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4