High-Throughput VLSI Architecture for GRAND

Abstract

Guessing Random Additive Noise Decoding (GRAND) is a recently proposed universal decoding algorithm for linear error correcting codes. Since GRAND does not depend on the structure of the code, it can be used for any code encountered in contemporary communication standards or may even be used for random linear network coding. This property makes this new algorithm particularly appealing. Instead of trying to decode the received vector, GRAND attempts to identify the noise that corrupted the codeword. To that end, GRAND relies on the generation of test error patterns that are successively applied to the received vector. In this paper, we propose the first hardware architecture for the GRAND algorithm. Considering GRAND with ABandonment (GRANDAB) that limits the number of test patterns, the proposed architecture only needs $2+\sum_{i=2}^{n} \left\lfloor\frac{i}{2}\right\rfloor$ time steps to perform the $\sum_{i=1}^3 \binom{n}{i}$ queries required when $\text{AB}=3$. For a code length of $128$, our proposed hardware architecture demonstrates only a fraction ($1.2\%$) of the total number of performed queries as time steps. Synthesis result using TSMC 65nm CMOS technology shows that average throughputs of $32$ Gbps to $64$ Gbps can be achieved at an SNR of $10$ dB for a code length of $128$ and code rates rate higher than $0.75$, transmitted over an AWGN channel. Comparisons with a decoder tailored for a $(79,64)$ BCH code show that the proposed architecture can achieve a slightly higher average throughput at high SNRs, while obtaining the same decoding performance.