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arXiv:2108.12563 · SiPS ... design and implementation - IEEE Workshop on Signal Processing Systems

High-Throughput VLSI Architecture for GRAND Markov Order

Syed Mohsin Abbas, Marwan Jalaleddine, Warren J. Gross

Published Oct 1, 2021• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/sips52927.2021.00036

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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 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 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> 0.5>0.5dB gain over the standard schedule at a block error rate≤10−5\le 10^{-5}≤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) has been proposed as an efficient and universal decoding technique for linear block codes [1]. A necessary element of the GRAND decoder is a set of noise sequences of lengthnnnequal to the code length. The decoded codeword is taken as the first valid codeword that results from the binary addition of the noise sequences, in order of likelihood, with the received word. For a binary code of lengthn\boldsymbol{n}nthere are2n2^{n}2nsuch noise sequences. Whenn\boldsymbol{n}nis large, it will typically be intractable to add every noise sequence during decoding. Moreover, these sequences exhibit a number of error bursts(m)(\boldsymbol{m})(m)and a total number of bit flips(l)(\boldsymbol{l})(l). In [1] the authors provide expressions to determine the probability of each error burst sequence for a two-state Markov channel model. The resulting decoder is called GRAND-Markov Order (GRAND-MO). The authors of [1] describe a GRAND-MO error pattern generator for the two-state Markov channel based upon sequential transition between(m,l)(\boldsymbol{m},\boldsymbol{l})(m,l)pairs, incrementingm\boldsymbol{m}mfirst, and then treating each value of l. In this paper we address a method of constructing the n-length noise sequences based upon integer compositions on the requiredlllbit flips as well as then−l\boldsymbol{n}-\boldsymbol{l}n−lnon-errors in the sequence. This method allows one to construct noise sequences in order of probability without the need to construct less likely noise sequences. A GRAND decoder may employ a limited number of noise sequences and abandon decoding upon finding a valid code word, or upon reaching an abandonment threshold without decoding success. In this way the most likely noise sequences can be prioritized in decoding.
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.
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.