Symbol-Level GRAND for High-Order Modulation Over Block Fading Channels

Guessing random additive noise decoding (GRAND) is a noise-centric decoding method, which is suitable for low-latency communications, as it supports error correction codes that generate short codewords. GRAND estimates transmitted codewords by guessing the error patterns that altered them during transmission. The guessing process requires the 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 block fading channels and proposes a more computationally efficient 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 expression that approximately computes the probability of occurrence of an error pattern and determines the order with which error patterns are tested. Analysis and simulation results demonstrate that symbol-level GRAND produces estimates of the transmitted codewords faster than the original GRAND at the cost of a small increase in memory requirements.