ORBGRAND: Soft-Decision Universal Decoding

• Ordered Reliability Bits GRAND (ORBGRAND) is a universal soft-decision decoding framework that exploits ordered bit reliabilities to approach near-ML performance in various channel conditions.
• The framework employs innovative noise-pattern enumeration and hardware-friendly, massively parallel architectures to minimize latency and query complexity.
• Extensions and fine-tuning strategies in ORBGRAND address channel uncertainties and non-Gaussian noise, enabling capacity-approaching performance in challenging environments.

Ordered Reliability Bits GRAND (ORBGRAND) is a universal soft-decision decoding framework for block codes, built on the principle of optimal or near-optimal noise pattern enumeration by leveraging reliability information derived from the channel output. The method generalizes the Guessing Random Additive Noise Decoding (GRAND) paradigm to fully exploit soft (or quantized-soft) channel observations, while maintaining code-agnostic applicability and architectural suitability for massive parallelization. Through algorithmic innovations and hardware-aware pattern generation, ORBGRAND provides near-maximal likelihood (ML) decoding performance across linear and non-linear codes, enables capacity-achieving universal decoding, and efficiently adapts to challenging channel scenarios such as imperfect channel state information (CSI), non-Gaussian noise, and correlated noise models.

1. Principle and Decoding Algorithm

The defining feature of ORBGRAND is its noise-focused, soft-input, universal decoding approach. For a received word $y\in\mathbb{R}^n$ (e.g., channel LLRs from BPSK over AWGN or higher-order modulations via bit-interleaved coded modulation), ORBGRAND computes bit reliabilities $\{|y_i|\}$ and produces a permutation $\pi$ such that $$|y_{\pi(1)}|\leq |y_{\pi(2)}|\leq\cdots\leq|y_{\pi(n)}|$$. Noise patterns $z\in\{0,1\}^n$ are then hypothesized in an order designed to approximate the maximum a posteriori (MAP) probability of the noise event.

The core enumeration is achieved by (a) fixing an order on the bit positions (according to reliability) and (b) generating error patterns in increasing "logistic weight," e.g.,

$LW(z) = \sum_{j:\,z_j=1} j,$

where $j$ indexes the sorted (permuted) bit positions. Each $z$ is applied by

$q = \operatorname{HD}(y) \oplus z,$

and a codeword membership test determines if $q\in\mathcal{C}$; decoding halts upon the first success (Duffy, 2020, Abbas et al., 2021, Duffy et al., 2022). Integer partitioning of $LW$ enables computationally minimal, on-the-fly pattern generation (Abbas et al., 2021, Abbas et al., 2021).

Hardware-friendly instantiations store a limited set of patterns (typically up to $Q\ll2^n$) in precomputed or LUT-based orderings, further reducing complexity and latency (Condo, 2021, Condo, 3 Jul 2024). Improved scheduling strategies such as iLWO or LA-iLWO adjust pattern priority to favor low-Hamming-weight events at moderate SNRs (Condo et al., 2021, Condo, 2021).

2. Capacity-Achieving and Theoretical Foundations

ORBGRAND with a zero-intercept linear reliability model and basic ordering is nearly capacity-achieving on memoryless binary-input channels, with the gap to channel capacity depending primarily on the quality of the reliability ranking (Li et al., 22 Jan 2024). Recent theoretical advances show that by companding the ranks using the inverse reliability cumulative distribution function (CDF), i.e., replacing the cost $\gamma_i = r_i/N$ with $\gamma_i = \Psi^{-1}(r_i/(N+1))$ where $\Psi(t) = \Pr(|T|\leq t)$, the resulting CDF-ORBGRAND achieves the exact mutual information of arbitrary binary-input memoryless channels—i.e., the symmetric capacity (Li et al., 29 Nov 2025). This result extends directly to multi-bit parallel channels via BICM, with analogous companding for each bit channel.

The achievable rate analysis for the standard ORBGRAND decoder is via the generalized mutual information (GMI) framework, confirming that ORBGRAND approaches or achieves capacity when well-calibrated, and is strictly capacity-achieving when using rank-companding via the empirical CDF (Li et al., 29 Nov 2025, Li et al., 22 Jan 2024, Yuan et al., 2022).

3. Practical Hardware Architectures

ORBGRAND is engineered for massive parallelism and high throughput, realized in VLSI/ASIC through a deeply pipelined architecture. Key modules include:

• Hard-decision circuit and reliability quantizer.
• Pipelined bitonic sorter (or equivalent) for rank computation.
• Pattern generator (integer partitioning logic or LUT-based) for on-the-fly error pattern synthesis.
• Parity-check calculator (syndrome calculator via XOR arrays) for codeword validation.

This parallelization enables throughputs up to 95.5 Gb/s and sub-30 ns worst-case latency for $[128,113]$ codes in advanced CMOS nodes (Condo, 3 Jul 2024). Multi-core implementations and dynamic clock gating further enhance energy efficiency and average-case performance. Code-agnostic programmability is achieved through parameterization of the parity-check (and, if needed, LUT) memories (Abbas et al., 2021, Condo, 3 Jul 2024, Condo, 2021).

Improved scheduling—via iLWO, LA-iLWO, or LUT-prioritized pattern lists—further reduces the query count and tightens the performance gap to ML at fixed budget (Condo, 2021, Condo et al., 2021). Segmented ORBGRAND exploits code structure to decompose the error pattern search space into syndrome-compatible subspaces, leading to substantial query reductions (Rowshan et al., 2023).

4. Extensions: Fine-Tuning, Channel Uncertainties, and Non-IID Noise

For short or intermediate block lengths where pattern ordering mismatch leads to loss versus ML decoding, several enhancements are effective:

• Fine-tuning by incorporating a small number $D$ of true reliability values into the test metric closes the gap to ML with negligible increase in complexity (Wan et al., 11 Jul 2025).
• RS-ORBGRAND reshuffles the order of queries by precomputing the expected posterior probabilities, reducing both average queries and the BLER gap to ML to as little as 0.1 dB (Wan et al., 29 Jan 2024).

ORBGRAND robustly adapts to channel uncertainties and non-Gaussian noise:

• In fading channels with imperfect channel estimation (CEE), running ORBGRAND in parallel with multiple candidate LLR vectors derived from neighborhood channel estimates, and then selecting the codeword that maximizes the posterior, yields multi-dB BLER improvements (5–7 dB) compared to naive decoders (Wiame et al., 17 Jun 2025).
• In impulsive, $\alpha$-stable, or interference-limited noise, using appropriate LLR models inside the ORBGRAND ranking, or switching to an errors-and-erasures strategy, gains 2–3 dB over standard AWGN-adapted decoding (Wiame et al., 30 Oct 2024).

ORBGRAND-AI generalizes the noise model to account for block (or symbol-level) correlation, using blockwise posterior metric computation and pattern generation under an approximate independence assumption. This substantially boosts error-correction capability in correlated channels (e.g., Gauss–Markov), obviating the need for capacity-reducing interleaving (Duffy et al., 2023, Feng et al., 10 Nov 2025).

5. Algorithmic and Schedule Optimization

Pattern scheduling is governed by a universal partial order (UPO): all test orderings must be a linear extension of UPO to maintain optimality properties (Condo et al., 2021). For practical budgets, iLWO (improved logistic weight order) and LUT-aided scheduling significantly enhance early pattern success probability and reduce BLER by up to 0.5 dB at very low error rates ($10^{-5}$ or below) (Condo, 2021, Condo et al., 2021).

Segmented ORBGRAND partitions the code into disjoint segments aligned with code constraints, generating only syndrome-compliant sub-patterns and combining them in a two-level integer partitioning hierarchy. This dramatically reduces redundant tests and enables further query complexity reductions by a factor of $2^p$ for $p$ independent partitions (Rowshan et al., 2023).

Recent techniques further bridge the ORBGRAND–SGRAND (true ML ordering) gap by hybridizing the initial ORB scan with a SGRAND residual tree search on the remaining pattern "envelope," merging the hardware-friendliness of ORBGRAND with the optimality guarantees of SGRAND (Wan et al., 2 Oct 2025).

6. Iterative and Soft-Output Decoding

ORBGRAND can be converted from a traditional hard-output decoder to a soft-input soft-output (SISO) iterative decoder by extending the candidate selection to include competitors for extrinsic information computation. Techniques such as iteration-dependent schedule adaptation, early-termination for competing codeword search, and budget allocation per iteration reduce total complexity by up to 85% with virtually no loss in BER (Condo, 2022).

ORBGRAND decoders thus enable low-latency, high-throughput, and near-ML performance not only for stand-alone block codes, but also when chained in iterative concatenated code architectures (e.g., staircase, turbo-like outer codes).

7. Performance Benchmarks and Impact

Comprehensive simulation and hardware reporting establish the following performance facts:

• ORBGRAND achieves BLER at or within $0.1$–$0.2$ dB of SGRAND/ML on a wide range of $(n,k)$ codes (BCH, CA-Polar, RLC, CRC-PAC), with only $O(10^2)$–$O(10^3)$ queries even at stringent BLER targets ($10^{-6}$–$10^{-7}$) (Duffy, 2020, Abbas et al., 2021, Duffy et al., 2022).
• In hardware, ORBGRAND VLSI cores attain up to $95$ Gb/s throughput and sub-$30$ ns latency for $n=128$, greatly outperforming list decoders such as CA-SCL in both speed ($\times49$) and energy efficiency ($\times32$) at similar error rates (Abbas et al., 2021, Condo, 3 Jul 2024, Condo, 2021).
• Under high SNR, segmented and fine-tuned variants further reduce query counts and close the residual performance gap to ML or SGRAND.
• In challenging channels (severe CEE, impulsive noise, or correlated noise), variant instantiations of ORBGRAND reliably realize several-dB BLER improvement compared to standard or code-structure-specific decoders (Wiame et al., 17 Jun 2025, Wiame et al., 30 Oct 2024, Duffy et al., 2023).

ORBGRAND thus sets a new standard for universal, high-performance, low-latency soft-decision decoding—enabling code-unified, programmable architectures needed for 5G/6G URLLC and other emerging high-reliability, low-latency applications.