LLR Approximation for Wireless Channels Based on Taylor Series and Its Application to BICM with LDPC Codes

TL;DR

This paper introduces a Taylor series-based approximation method for channel LLRs in wireless communication, simplifying calculations while maintaining accuracy, and demonstrates its effectiveness in BICM with LDPC codes.

Contribution

It presents a novel Taylor series-based approach for approximating channel LLRs that reduces complexity and improves accuracy in wireless communication systems.

Findings

Approximation closely matches exact LLR calculations.

Significantly reduces computational complexity.

Enhances error rate performance in BICM with LDPC codes.

Abstract

A new approach for the approximation of the channel log-likelihood ratio (LLR) for wireless channels based on Taylor series is proposed. The approximation is applied to the uncorrelated flat Rayleigh fading channel with unknown channel state information at the receiver. It is shown that the proposed approximation greatly simplifies the calculation of channel LLRs, and yet provides results almost identical to those based on the exact calculation of channel LLRs. The results are obtained in the context of bit-interleaved coded modulation (BICM) schemes with low-density parity-check (LDPC) codes, and include threshold calculations and error rate performance of finite-length codes. Compared to the existing approximations, the proposed method is either significantly less complex, or considerably more accurate.