Supporting ultra-reliable and low-latency communication (URLLC) is a challenge in current wireless systems. Channel codes that generate large codewords improve reliability but necessitate the use of interleavers, which introduce undesirable latency. Only short codewords can eliminate the requirement for interleaving and reduce decoding latency. This paper suggests a coding and decoding method which, when combined with the high spectral efficiency of spatial multiplexing, can provide URLLC over a fading channel. Random linear coding and modulation are used to transmit information over a massive multiple-input multiple-output (mMIMO) uplink channel, followed by zero-forcing detection and guessing random additive noise decoding (GRAND) at a receiver. This work considers symbol-level GRAND, which is a variant of GRAND that was originally proposed for single-antenna systems employing square M-ary quadrature amplitude modulation, and generalizes it to schemes that combine spatial multiplexing with any M-ary modulation method. The paper studies the impact of the orthogonality defect of the underlying mMIMO lattice on symbol-level GRAND, and proposes to leverage side-information that comes from the mMIMO channel-state information and relates to the reliability of each receive antenna. Additionally, a lightweight membership test is introduced to reduce the number of error patterns that undergo full membership tests, by making use of a row in the parity-check matrix that eliminates candidate error patterns. All proposals reduce the decoding speed without compromising the decoding performance. The proposed decoder operating at the symbol level, when combined with antenna sorting and syndrome-constrained decoding, has the potential to reduce complexity by 90% when compared to bit-level GRAND in some of the tested configurations.

This work is funded by national funds through FCT, I.P., and, when eligible, co-funded by EU funds under project/support UID/50008/2025 – Instituto de Telecomunicac¸oes. Sahar Allahkaram is funded by a merit scholarship from Iscte-IUL.

Antenna sorting,Constrained decoding,Guessing random additive noise decoding (GRAND),Massive multiple-input multiple-output (mMIMO),Random linear codes (RLCs),Symbol-level decoding,Ultra-reliable and low-latency communications (URLLC)

• Electrical Engineering, Electronic Engineering, Information Engineering - Engineering and Technology