Guessing random additive noise decoding (GRAND) is a code-agnostic decoding method that iteratively guesses the noise pattern affecting the received codeword. The number of noise sequences to test depends on the noise realization. Thus, GRAND exhibits random runtime which results in nondeterministic throughput. However, real-time systems must process the incoming data at a fixed rate, necessitating a fixed-throughput decoder in order to avoid losing data. We propose a first-in first-out (FIFO) scheduling architecture that enables a fixed throughput while improving the block error rate (BLER) compared to the common approach of imposing a maximum runtime constraint per received codeword. Moreover, we demonstrate that the average throughput metric of GRAND-based hardware implementations typically provided in the literature can be misleading as one needs to operate at approximately one order of magnitude lower throughput to achieve the BLER of an unconstrained decoder.Guessing random additive noise decoding (GRAND) is a code-agnostic decoding method that iteratively guesses the noise pattern affecting the received codeword. The number of noise sequences to test depends on the noise realization. Thus, GRAND exhibits random runtime which results in nondeterministic throughput. However, real-time systems must process the incoming data at a fixed rate, necessitating a fixed-throughput decoder in order to avoid losing data. We propose a first-in first-out (FIFO) scheduling architecture that enables a fixed throughput while improving the block error rate (BLER) compared to the common approach of imposing a maximum runtime constraint per received codeword. Moreover, we demonstrate that the average throughput metric of GRAND-based hardware implementations typically provided in the literature can be misleading as one needs to operate at approximately one order of magnitude lower throughput to achieve the BLER of an unconstrained decoder.

IEEE International Symposium on Circuits and Systems proceedingsMay 25, 20250 citations

Fixed-Throughput GRAND with FIFO Scheduling

Christen, Filippo, Darja Nonaca, Christoph Studer

Jan 1, 20250 citations

A Fixed Latency ORBGRAND Decoder Architecture With LUT-Aided Error-Pattern Scheduling

Carlo Condo

Guessing Random Additive Noise Decoding (GRAND) is a universal decoding algorithm that has been recently proposed as a practical way to perform maximum likelihood decoding. It generates a sequence of possible error patterns and applies them to the received vector, checking if the result is a valid codeword. Ordered reliability bits GRAND (ORBGRAND) improves on GRAND by considering soft information received from the channel. Both GRAND and ORBGRAND have been implemented in hardware, focusing on average performance, sacrificing worst case throughput and latency. In this work, an improved pattern schedule for ORBGRAND is proposed. It provides $> 0.5$ dB gain over the standard schedule at a block error rate $\le 10^{-5}$ , and outperforms more complex GRAND flavors with a fraction of the complexity. The proposed schedule is used within a novel code-agnositic decoder architecture: the decoder guarantees fixed high throughput and low latency, making it attractive for latency-constrained applications. It outperforms the worst-case performance of decoders by orders of magnitude, and outperforms many best-case figures. Decoding a code of length 128, it achieves a throughput of 79.21 Gb/s with 58.49 ns latency, yielding better energy efficiency and comparable area efficiency with respect to the state of the art.Guessing Random Additive Noise Decoding (GRAND) is a universal decoding algorithm that has been recently proposed as a practical way to perform maximum likelihood decoding. It generates a sequence of possible error patterns and applies them to the received vector, checking if the result is a valid codeword. Ordered reliability bits GRAND (ORBGRAND) improves on GRAND by considering soft information received from the channel. Both GRAND and ORBGRAND have been implemented in hardware, focusing on average performance, sacrificing worst case throughput and latency. In this work, an improved pattern schedule for ORBGRAND is proposed. It provides$> 0.5$dB gain over the standard schedule at a block error rate$\le 10^{-5}$, and outperforms more complex GRAND flavors with a fraction of the complexity. The proposed schedule is used within a novel code-agnositic decoder architecture: the decoder guarantees fixed high throughput and low latency, making it attractive for latency-constrained applications. It outperforms the worst-case performance of decoders by orders of magnitude, and outperforms many best-case figures. Decoding a code of length 128, it achieves a throughput of 79.21 Gb/s with 58.49 ns latency, yielding better energy efficiency and comparable area efficiency with respect to the state of the art.

arXiv:2111.08134IEEE Transactions on Circuits and Systems I Regular PapersFeb 17, 202263 citations

High-Throughput VLSI Architecture for GRAND Markov Order

Syed Mohsin Abbas, Marwan Jalaleddine, Warren J. Gross

Guessing Random Additive Noise Decoding (GRAND) is a recently proposed Maximum Likelihood (ML) decoding technique. Irrespective of the structure of the error correcting code, GRAND tries to guess the noise that corrupted the codeword in order to decode any linear error-correcting block code. GRAND Markov Order (GRAND-MO) is a variant of GRAND that is useful to decode error correcting code transmitted over communication channels with memory which are vulnerable to burst noise. Usually, interleavers and de-interleavers are used in communication systems to mitigate the effects of channel memory. Interleaving and de-interleaving introduce undesirable latency, which increases with channel memory. To prevent this added latency penalty, GRAND-MO can be directly used on the hard demodulated channel signals. This work reports the first GRAND-MO hardware architecture which achieves an average throughput of up to 52 Gbps and 64 Gbps for a code length of 128 and 79 respectively. Compared to the GRANDAB, hard-input variant of GRAND, the proposed architecture achieves 3 dB gain in decoding performance for a target FER of 10−5. Similarly, comparing the GRAND-MO decoder with a decoder tailored for a (79,64) BCH code showed that the proposed architecture achieves 33% higher worst case throughput and 2 dB gain in decoding performance.Guessing Random Additive Noise Decoding (GRAND) is a recently proposed Maximum Likelihood (ML) decoding technique. Irrespective of the structure of the error correcting code, GRAND tries to guess the noise that corrupted the codeword in order to decode any linear error-correcting block code. GRAND Markov Order (GRAND-MO) is a variant of GRAND that is useful to decode error correcting code transmitted over communication channels with memory which are vulnerable to burst noise. Usually, interleavers and de-interleavers are used in communication systems to mitigate the effects of channel memory. Interleaving and de-interleaving introduce undesirable latency, which increases with channel memory. To prevent this added latency penalty, GRAND-MO can be directly used on the hard demodulated channel signals. This work reports the first GRAND-MO hardware architecture which achieves an average throughput of up to 52 Gbps and 64 Gbps for a code length of 128 and 79 respectively. Compared to the GRANDAB, hard-input variant of GRAND, the proposed architecture achieves 3 dB gain in decoding performance for a target FER of 10−5. Similarly, comparing the GRAND-MO decoder with a decoder tailored for a (79,64) BCH code showed that the proposed architecture achieves 33% higher worst case throughput and 2 dB gain in decoding performance.

arXiv:2108.12563SiPS ... design and implementation - IEEE Workshop on Signal Processing SystemsOct 1, 202120 citations

Performance Analysis and Optimal Design of ORB-Type GRAND Algorithms

Li Wan, Wenyi Zhang

Guessing Random Additive Noise Decoding (GRAND) performs decoding by sequentially guessing channel error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) is a notable instance suitable for efficient implementation, as it schedules EPs solely according to the ranking of soft channel outputs. In this paper, we generalize this principle to a broader class of GRAND algorithms whose testing order depends only on reliability ranking, referred to as ORB-type GRAND. We develop a unified analytical framework based on a key quantity termed the average guessing posterior (AGP), which captures the effectiveness of each EP and reduces decoding into an ordering problem over the EP space. For random code ensembles, we derive exact expressions for the block error rate (BLER), stopping-time distribution, and average number of tests under a fixed test budget. The analysis separates target-miss and target-preemption errors and shows that ordering EPs by non-increasing AGP is optimal over the EP set under consideration. For fixed linear block codes, we derive the BLER expression that isolates the code-dependent target-preemption term and characterize this term through higher-order weight relationships of codeword tuples, with a computable first-order upper bound as a useful special case. Guided by these insights, we formulate ReShuffled-ORBGRAND (RS-ORBGRAND) as an offline AGP-based reshuffling scheme. Numerical results for the Bose--Chaudhuri--Hocquenghem (BCH) $(127,113)$ code show that RS-ORBGRAND consistently improves existing ORB-type GRAND algorithms and lies within $0.1$ ~dB of a maximum-likelihood decoding lower-bound benchmark at a BLER of $10^{-6}$ .Guessing Random Additive Noise Decoding (GRAND) performs decoding by sequentially guessing channel error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) is a notable instance suitable for efficient implementation, as it schedules EPs solely according to the ranking of soft channel outputs. In this paper, we generalize this principle to a broader class of GRAND algorithms whose testing order depends only on reliability ranking, referred to as ORB-type GRAND. We develop a unified analytical framework based on a key quantity termed the average guessing posterior (AGP), which captures the effectiveness of each EP and reduces decoding into an ordering problem over the EP space. For random code ensembles, we derive exact expressions for the block error rate (BLER), stopping-time distribution, and average number of tests under a fixed test budget. The analysis separates target-miss and target-preemption errors and shows that ordering EPs by non-increasing AGP is optimal over the EP set under consideration. For fixed linear block codes, we derive the BLER expression that isolates the code-dependent target-preemption term and characterize this term through higher-order weight relationships of codeword tuples, with a computable first-order upper bound as a useful special case. Guided by these insights, we formulate ReShuffled-ORBGRAND (RS-ORBGRAND) as an offline AGP-based reshuffling scheme. Numerical results for the Bose--Chaudhuri--Hocquenghem (BCH)$(127,113)$ code show that RS-ORBGRAND consistently improves existing ORB-type GRAND algorithms and lies within $0.1$~dB of a maximum-likelihood decoding lower-bound benchmark at a BLER of $10^{-6}$.

arXiv:2606.28030Jun 26, 20260 citations

High-Throughput VLSI Architecture for Soft-Decision Decoding with ORBGRAND

Syed Mohsin Abbas, Thibaud Tonnellier, Furkan Ercan +2 more

Guessing Random Additive Noise Decoding (GRAND) is a recently proposed approximate Maximum Likelihood (ML) decoding technique that can decode any linear error-correcting block code. Ordered Reliability Bits GRAND (ORBGRAND) is a powerful variant of GRAND, which outperforms the original GRAND technique by generating error patterns in a specific order. Moreover, their simplicity at the algorithm level renders GRAND family a desirable candidate for applications that demand very high throughput. This work reports the first-ever hardware architecture for ORBGRAND, which achieves an average throughput of up to 42.5 Gbps for a code length of 128 at an SNR of 10 dB. Moreover, the proposed hardware can be used to decode any code provided the length and rate constraints. Compared to the state-of-the-art fast dynamic successive cancellation flip decoder (Fast-DSCF) using a 5G polar (128,105) code, the proposed VLSI implementation has 49× more average throughput while maintaining similar decoding performance.Guessing Random Additive Noise Decoding (GRAND) is a recently proposed approximate Maximum Likelihood (ML) decoding technique that can decode any linear error-correcting block code. Ordered Reliability Bits GRAND (ORBGRAND) is a powerful variant of GRAND, which outperforms the original GRAND technique by generating error patterns in a specific order. Moreover, their simplicity at the algorithm level renders GRAND family a desirable candidate for applications that demand very high throughput. This work reports the first-ever hardware architecture for ORBGRAND, which achieves an average throughput of up to 42.5 Gbps for a code length of 128 at an SNR of 10 dB. Moreover, the proposed hardware can be used to decode any code provided the length and rate constraints. Compared to the state-of-the-art fast dynamic successive cancellation flip decoder (Fast-DSCF) using a 5G polar (128,105) code, the proposed VLSI implementation has 49× more average throughput while maintaining similar decoding performance.

arXiv:2105.07115IEEE International Conference on Acoustics Speech and Signal ProcessingMay 13, 202131 citations

> 0.5

dB gain over the standard schedule at a block error rate

\le 10^{-5}

, and outperforms more complex GRAND flavors with a fraction of the complexity. The proposed schedule is used within a novel code-agnositic decoder architecture: the decoder guarantees fixed high throughput and low latency, making it attractive for latency-constrained applications. It outperforms the worst-case performance of decoders by orders of magnitude, and outperforms many best-case figures. Decoding a code of length 128, it achieves a throughput of 79.21 Gb/s with 58.49 ns latency, yielding better energy efficiency and comparable area efficiency with respect to the state of the art.

(127,113)

code show that RS-ORBGRAND consistently improves existing ORB-type GRAND algorithms and lies within

0.1

~dB of a maximum-likelihood decoding lower-bound benchmark at a BLER of

10^{-6}