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Parallelism Empowered Guessing Random Additive Noise Decoding

Li Wan, Huarui Yin, Wenyi Zhang

TL;DR

The paper tackles the challenge of achieving ML decoding with GRAND while leveraging hardware parallelism. It introduces the EP tree to unify error pattern representations and enable parallel exploration, delivering a parallel SGRAND that preserves ML and a suite of acceleration techniques (pruning, tree-based computation, early termination). It further enhances ORBGRAND by integrating the EP-tree framework into a hybrid method that attains ML-like performance with minimal overhead. Simulation results show substantial latency reductions, with 3.75× speedup for parallel SGRAND and up to 4.8× for the hybrid enhanced ORBGRAND, highlighting practical potential for URLLC and other latency-constrained settings. The work lays a path toward hardware-realizable, universal decoders that combine ML optimality with scalable parallelism.

Abstract

Advances in parallel hardware platforms have motivated the development of efficient universal decoders capable of meeting stringent throughput and latency requirements. Guessing Random Additive Noise Decoding (GRAND) is a recently proposed decoding paradigm that sequentially tests Error Patterns (EPs) until finding a valid codeword. While Soft GRAND (SGRAND) achieves maximum-likelihood (ML) decoding, its inherently sequential nature hinders parallelism and results in high decoding latency. In this work, we utilize a unified binary tree representation of EPs, termed the EP tree, which enables compact representation, efficient manipulation, and parallel exploration. Building upon this EP tree representation, we propose a parallel design of SGRAND, preserving its ML optimality while significantly reducing decoding latency through pruning strategies and tree-based computation. Furthermore, we develop a hybrid GRAND algorithm that enhances Ordered Reliability Bits (ORB) GRAND with the EP tree representation, thereby achieving ML decoding with minimal additional computational cost beyond ORBGRAND while retaining parallel efficiency. Numerical experiments demonstrate that parallel SGRAND achieves a $3.75\times$ acceleration compared to serial implementation, while the hybrid enhanced method achieves a $4.8\times$ acceleration, with further gains expected under hardware mapping.

Parallelism Empowered Guessing Random Additive Noise Decoding

TL;DR

The paper tackles the challenge of achieving ML decoding with GRAND while leveraging hardware parallelism. It introduces the EP tree to unify error pattern representations and enable parallel exploration, delivering a parallel SGRAND that preserves ML and a suite of acceleration techniques (pruning, tree-based computation, early termination). It further enhances ORBGRAND by integrating the EP-tree framework into a hybrid method that attains ML-like performance with minimal overhead. Simulation results show substantial latency reductions, with 3.75× speedup for parallel SGRAND and up to 4.8× for the hybrid enhanced ORBGRAND, highlighting practical potential for URLLC and other latency-constrained settings. The work lays a path toward hardware-realizable, universal decoders that combine ML optimality with scalable parallelism.

Abstract

Advances in parallel hardware platforms have motivated the development of efficient universal decoders capable of meeting stringent throughput and latency requirements. Guessing Random Additive Noise Decoding (GRAND) is a recently proposed decoding paradigm that sequentially tests Error Patterns (EPs) until finding a valid codeword. While Soft GRAND (SGRAND) achieves maximum-likelihood (ML) decoding, its inherently sequential nature hinders parallelism and results in high decoding latency. In this work, we utilize a unified binary tree representation of EPs, termed the EP tree, which enables compact representation, efficient manipulation, and parallel exploration. Building upon this EP tree representation, we propose a parallel design of SGRAND, preserving its ML optimality while significantly reducing decoding latency through pruning strategies and tree-based computation. Furthermore, we develop a hybrid GRAND algorithm that enhances Ordered Reliability Bits (ORB) GRAND with the EP tree representation, thereby achieving ML decoding with minimal additional computational cost beyond ORBGRAND while retaining parallel efficiency. Numerical experiments demonstrate that parallel SGRAND achieves a acceleration compared to serial implementation, while the hybrid enhanced method achieves a acceleration, with further gains expected under hardware mapping.

Paper Structure

This paper contains 25 sections, 5 theorems, 24 equations, 9 figures, 4 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Transmission Model
  5. GRAND
  6. EP Tree Representation and Parallelization of SGRAND
  7. Error Pattern Tree
  8. Revisiting SGRAND
  9. Implementation and Complexity
  10. Parallel SGRAND
  11. Analysis and Design Considerations
  12. Accelerating Parallel SGRAND
  13. Pruning Strategy to Eliminate Unnecessary Tests
  14. Leveraging Tree Structure to Accelerate Computation
  15. Early Termination Based on Code Weight
  16. ...and 10 more sections

Key Result

Proposition 1

We define the soft weight of an EP $\underline{e}$ as $\zeta(\underline{e}) = \sum_{i:e_i = 1} \ell_i$. If we set the maximum query limit to $T = 2^N$ and generate $\underline{e}(t)$ for $1 \leq t \leq 2^N$ such that the sequence $\{\zeta(\underline{e}(t))\}_{t = 1,\ldots,2^N}$ is monotonically non-

Figures (9)

  • Figure 1: Example \ref{['ex:tree_sgrand']}: EP tree when $\underline{r}=(3,1,2,4)$. Red nodes: $\mathcal{S}$ at $t=5$; black nodes: examined; gray nodes: not yet retrieved.
  • Figure 2: Operations on the min-heap at $t=6$ (continuing Example \ref{['ex:tree_sgrand']}).
  • Figure 3: Schematic diagram of parallel SGRAND algorithm
  • Figure 4: Schematic diagram of the decoding process of Algorithm \ref{['alg:ORB_with_SGRAND']}.
  • Figure 5: Example \ref{['ex:4']}: Elements of $\mathcal{S}_{0}$ are marked in red for subsequent parallel SGRAND decoding.
  • ...and 4 more figures

Theorems & Definitions (13)

  • Proposition 1
  • Definition 1: EP tree
  • Example 1
  • Example 2
  • Remark 1
  • Theorem 1
  • Lemma 1: taipale1991improvement
  • Example 3
  • Definition 2: $\gamma$-based $\tilde{\mathcal{E}}_{\text{ORB}}$
  • Proposition 2
  • ...and 3 more