GRAND Massive Parallel Decoding Framework for Low Latency in Beyond 5G

TL;DR

This work addresses ultra-low-latency decoding for beyond-5G control channels by introducing a massively parallel GRAND framework. It combines a new likelihood function for $M$-QAM that reduces the symbol-error pattern space to $O(4^{N/ ext{log}_2 M})$ with a massively parallel matrix–vector multiply that computes $oldsymbol{H}oldsymbol{c}^T$ in $O( ext{log}_2 N)$ steps. The method is applied to 5G NR Polar codes with rate $R=1/2$ across codeword lengths $N leftarrow ext{32 to 1024}$ and modulation orders up to $4096$-QAM, and is shown to achieve low latency by distributing the search over up to $4^S$ parallel instances, yielding a latency bound of $2n+2S+4$ clock cycles. The approach demonstrates competitive BLER performance across high-order modulations while preserving practicality for both short and long codewords, highlighting its potential to enable rapid, reliable control-channel decoding in beyond-5G networks.

Abstract

We propose a massive parallel decoding GRAND framework. The framework introduces two novelties: 1. A likelihood function for $M$-QAM demodulated signals that effectively reduces the symbol error pattern space from $\mathcal{O}(5^{N/\log_2 M})$ down to $\mathcal{O}(4^{N/\log_2 M})$; and 2. A massively parallel matrix-vector multiplication for matrices of size $K\times N$ ($K \leq N$) that performs the multiplication in just $\mathcal{O}(\log_2 N)$ steps. We then apply the proposed GRAND approach to codes and operational modulation techniques used in the current 5G NR standard. Our framework is applicable not just to short codewords but to the full range of codewords from 32 bits up to 1024 bits used in the control channels of 5G NR. We also present simulation results with parity-check matrices of Polar codes with rate $R=1/2$ obtained from the 5G NR universal reliability sequence.

Figures (5)

• Figure 1: A 16-QAM constellation with associated Gray code for 4-bit sequences.
• Figure 2: Likelihood function $\mathcal{L}(r, s)$ and Near Neighbours Errors in our approach.
• Figure 3: The parity check matrix $\mathbf{H}_{32}$ of dimensions $16 \times 32$. Every coloured square represents 1, and every blank square represents 0.
• Figure 4: Simulation results: Block Error Rate (BLER) for the proposed GRAND-like approach for decoding Polar codes with codeword lengths $N = 32, \ldots, 1024$ bits for different $M$-QAM modulations.
• Figure :

Theorems & Definitions (7)

• Definition 2.1: Polar codes arikan2009channel
• Definition 2.2
• Definition 3.1
• Definition 3.2
• Corollary 3.1
• Theorem 3.1
• Proposition 3.1