Symbol-Level GRAND for High-Order Modulation over Flat Fading Channels

Guessing random additive noise decoding (GRAND) is a noise-centric decoding method, which is suitable for ultra-reliable low-latency communications, as it supports high-rate error correction codes that generate short-length codewords. GRAND estimates transmitted codewords by guessing the error patterns that altered them during transmission. The guessing process requires the generation and testing of error patterns that are arranged in increasing order of Hamming weight. This approach is fitting for binary transmission over additive white Gaussian noise channels. This letter considers transmission of coded and modulated data over flat fading channels and proposes a variant of GRAND, which leverages information on the modulation scheme and the fading channel. In the core of the proposed variant, referred to as symbol-level GRAND, is an analytical expression that computes the probability of occurrence of an error pattern and determines the order with which error patterns are tested. Simulation results demonstrate that symbol-level GRAND produces estimates of the transmitted codewords notably faster than the original GRAND at the cost of a small increase in memory requirements.