Guessing random additive noise decoding for digital data communication

This monograph presents guessing random additive noise decoding (GRAND), a novel approach to error correction that has rapidly transitioned from theoretical development to hardware implementation. Unlike traditional error correction paradigms that co-design codes and decoders, GRAND operates on a code-agnostic basis by systematically guessing noise patterns in decreasing order of likelihood and querying whether inverting each guess from a received sequence yields a valid codeword. This approach enables maximum likelihood decoding for any linear or non-linear code with moderate redundancy. A distinctive feature of GRAND algorithms with soft input is their ability to generate accurate blockwise soft output in the form of probabilistic estimates of decoding correctness, even with a single decoding. This capability surpasses conventional approximations and enables critical applications including upgrading CRC codes from error detection to error correction, reducing undetected error rates, enabling approximate query orders and facilitating soft-input soft-output iterative decoding of long, powerful concatenated codes. The monograph systematically explains the theoretical foundations, algorithmic variants and hardware implementation principles that have enabled GRAND’s remarkably fast path from conception to multiple taped-out application-specific integrated circuits. Through an explanation of query ordering strategies for both hard and soft input scenarios, performance evaluation across various codes and applications to iterative decoding, this work elucidates why GRAND’s inherent parallelizability and elegant mathematical properties make it suitable for efficient circuit implementation. The treatment is designed to clarify fundamental principles while providing practical insights for researchers and engineers working in error correction coding with an eye towards VLSI design.