Ordered Reliability Bits Guessing Random Additive Noise Decoding

Duffy, Ken R.; An, Wei; Médard, Muriel

doi:10.1109/tsp.2022.3203251

Cited by 60 publications

(18 citation statements)

References 73 publications

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“…Although these results have been rigorously proven for uniform-at-random codes as n → ∞, experimental applications using structured linear codes of small block-length, and also RLCs in particular, have produced striking results [11], [21]- [24], consistent with these theoretical guarantees.…”

Section: A Decoding Classical Rlcs By Noise Guessingmentioning

confidence: 76%

Quantum Error Correction via Noise Guessing Decoding

Cruz¹,

Monteiro²,

Coutinho³

2022

Preprint

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Quantum error correction codes (QECCs) play a central role both in quantum communications and in quantum computation, given how error-prone quantum technologies are. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code lengths and code rates, limiting their adaptability to changing requirements. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime, for any chosen code length and when the code rate is sufficiently high.A recently proposed strategy for decoding classical codes called GRAND (guessing random additive noise decoding) opened doors to decoding classical random linear codes (RLCs) that perform near the capacity of the finite blocklength regime. By making use of the noise statistics, GRAND is a noise-centric efficient universal decoder for classical codes, providing there is a simple code membership test. These conditions are particularly suitable for quantum systems and therefore the paper extends these concepts to quantum random linear codes (QRLCs), which were known to be possible to construct but whose decoding was not yet feasible. By combining QRLCs and a newly proposed quantum GRAND, this paper shows that decoding versatile quantum error correction is possible, allowing for QECCs that are simple to adapt on the fly to changing conditions. The paper starts by assessing the minimum number of gates in the coding circuit needed to reach the QRLCs' asymptotic performance, and subsequently proposes a quantum GRAND algorithm that makes use of quantum noise statistics, not only to build an adaptive code membership test, but also to efficiently implement syndrome decoding.

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Section: A Decoding Classical Rlcs By Noise Guessingmentioning

confidence: 76%

Quantum Error Correction via Noise Guessing Decoding

Cruz¹,

Monteiro²,

Coutinho³

2022

Preprint

View full text Add to dashboard Cite

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“…An ability to find the symbol that is in error and correcting it, or at least replacing it with one of the correct length, decreases both symbol and bit error rates. At this point, we draw inspiration from GRAND [19]- [21].…”

Section: Demodulation and Length Correctionmentioning

confidence: 99%

“…As for the nonuniform constellation design approach with sublattices, one needs to design a suitable code that would yield the channel optimal distribution. A core contribution of this paper is a new light-weight scheme based on the recently introduced Guessing Random Additive Noise Decoding (GRAND) [19]- [21] that enables the translation of improved symbol error rates to improved bit error rates through low complexity length correction based on symbol padding. While padding schemes have previously been proposed, e.g.…”

Section: Introductionmentioning

confidence: 99%

GRAND-assisted Optimal Modulation

Ozaydin¹,

Médard²,

Duffy³

2022

Preprint

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Optimal modulation (OM) schemes for Gaussian channels with peak and average power constraints are known to require nonuniform probability distributions over signal points, which presents practical challenges. An established way to map uniform binary sources to non-uniform symbol distributions is to assign a different number of bits to different constellation points. Doing so, however, means that erroneous demodulation at the receiver can lead to bit insertions or deletions that result in significant binary error propagation. In this paper, we introduce a light-weight variant of Guessing Random Additive Noise Decoding (GRAND) to resolve insertion and deletion errors at the receiver by using a simple padding scheme. Performance evaluation demonstrates that our approach results in an overall gain in demodulated bit-error-rate of over 2 dB Eb/N0 when compared to 128-Quadrature Amplitude Modulation (QAM). The GRAND-aided OM scheme outperforms coding with a lowdensity parity check code of the same average rate as that induced by our simple padding.

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“…Algorithm 1: ORBGRAND [8] Input: C: code membership function T: query threshold 𝑦 𝑛 : demodulated bits 𝑟 𝑛 :order of bit reliabilities Result: 𝑐 *,𝑛 : decoded codeword d: flag to indicate that a decoding is found q: number of iterations until a decoding is found Initialization: q←0, d ← 0; while 𝑞 < 𝑇 do 𝑧 𝑛 ← Next most likely noise sequence assuming that greater bit position = greater reliability…”

Section: Guess-based Decodingmentioning

confidence: 99%

Section: Decision Regionsmentioning

confidence: 99%

GRAND-assisted Optimal Modulation

Ozaydin

Médard

Duffy

2022

GLOBECOM 2022 - 2022 IEEE Global Communications Conference

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For Gaussian channels with peak and average power constraints the optimal modulation (OM) schemes are known to have nonuniform probability distributions over the signal points. An established way to obtain these distributions is assigning different number of bits to different constellation points. However, this method leads to challenges in demodulation as if a symbol is identified falsely, due to the different bit lengths of symbols, bit insertions or deletions may occur which may in return cause error propagation. Hence, the difficulty of realizing the channel optimal distributions on constellation signals impeded OM from becoming widely utilized in communication systems. In this thesis, we propose a practical system for OM that uses only a simple padding scheme instead of the complex mechanisms in the current literature. A guess-based error correction demodulator lies at the core of the proposed system. Together with the padding scheme of our choice, our novel light-weight variant of Guessing Random Additive Noise Decoding (GRAND) demodulator protects the system against insertions and deletions. We display that with our approach an overall gain of up to 2 dB in energy per bit over noise spectral density (𝐸 𝑏 /𝑁 0 ) is achievable compared to Quadrature Amplitude Modulation (QAM) with the same number of points.

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Ordered Reliability Bits Guessing Random Additive Noise Decoding

Cited by 60 publications

References 73 publications

Quantum Error Correction via Noise Guessing Decoding

Quantum Error Correction via Noise Guessing Decoding

GRAND-assisted Optimal Modulation

GRAND-assisted Optimal Modulation

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