Quantized Guessing Random Additive Noise Decoding

We introduce a soft-detection variant of Guessing Random Additive Noise Decoding (GRAND) called Quantized GRAND (QGRAND) that can efficiently decode any moderate redundancy block-code of any length in an algorithm that is suitable for highly parallelized implementation in hardware. QGRAND can avail of any level of quantized soft information, is established to be almost capacity achieving, and is shown to provide near maximum likelihood decoding performance when provided with five or more bits of soft information per received bit

URLLC with Coded Massive MIMO via Random Linear Codes and GRAND

A present challenge in wireless communications is the assurance of ultra-reliable and low-latency communication (URLLC). While the reliability aspect is well known to be improved by channel coding with long codewords, this usually implies using interleavers, which introduce undesirable delay. Using short codewords is a needed change to minimizing the decoding delay. This work proposes the combination of a coding and decoding scheme to be used along with spatial signal processing as a means to provide URLLC over a fading channel. The paper advocates the use of random linear codes (RLCs) over a massive MIMO (mMIMO) channel with standard zero-forcing detection and guessing random additive noise decoding (GRAND). The performance of several schemes is assessed over a mMIMO flat fading channel. The proposed scheme greatly outperforms the equivalent scheme using 5G's polar encoding and decoding for signal-to-noise ratios (SNR) of interest. While the complexity of the polar code is constant at all SNRs, using RLCs with GRAND achieves much faster decoding times for most of the SNR range, further reducing latency

URLLC with coded massive MIMO via random linear codes and GRAND

A present challenge in wireless communications is the assurance of ultra-reliable and low-latency communication (URLLC). While the reliability aspect is well known to be improved by channel coding with long codewords, this usually implies using interleavers, which introduce undesirable delay. Using short codewords is a needed change to minimizing the decoding delay. This work proposes the combination of a coding and decoding scheme to be used along with spatial signal processing as a means to provide URLLC over a fading channel. The paper advocates the use of random linear codes (RLCs) over a massive MIMO (mMIMO) channel with standard zero-forcing detection and guessing random additive noise decoding (GRAND). The performance of several schemes is assessed over a mMIMO flat fading channel. The proposed scheme greatly outperforms the equivalent scheme using 5G’s polar encoding and decoding for signal-to-noise ratios (SNR) of interest. While the complexity of the polar code is constant at all SNRs, using RLCs with GRAND achieves much faster decoding times for most of the SNR range, further reducing latency.info:eu-repo/semantics/acceptedVersio

Confident decoding with GRAND

We establish that during the execution of any Guessing Random Additive Noise Decoding (GRAND) algorithm, an interpretable, useful measure of decoding confidence can be evaluated. This measure takes the form of a log-likelihood ratio (LLR) of the hypotheses that, should a decoding be found by a given query, the decoding is correct versus its being incorrect. That LLR can be used as soft output for a range of applications and we demonstrate its utility by showing that it can be used to confidently discard likely erroneous decodings in favor of returning more readily managed erasures. As an application, we show that feature can be used to compromise the physical layer security of short length wiretap codes by accurately and confidently revealing a proportion of a communication when code-rate is above capacity

Quantum Error Correction via Noise Guessing Decoding

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