Related papers: Upgrade error detection to prediction with GRAND
Proposals have been made to reduce the guesswork of Guessing Random Additive Noise Decoding (GRAND) for binary linear codes by leveraging codebook structure at the expense of degraded block error rate (BLER). We establish one can preserve…
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…
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,…
Channel decoding is a challenging task in communication channels exhibiting memory effects. In this work, we apply the recently proposed decoding paradigm of guessing random additive noise decoding (GRAND) to channels with memory, focusing…
We establish that a large, flexible class of long, high redundancy error correcting codes can be efficiently and accurately decoded with guessing random additive noise decoding (GRAND). Performance evaluation demonstrates that it is…
In addition to a proposed codeword, error correction decoders that provide blockwise soft output (SO) return an estimate of the likelihood that the decoding is correct. Following Forney, such estimates are traditionally only possible for…
Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only…
Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, the size of the search space and consequently the decoding complexity grows exponentially, making it impractical to be…
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…
Guessing Random Additive Noise Decoding (GRAND) is a universal framework for decoding all block codes by testing candidate error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) facilitates parallel implementation of GRAND by…
The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and…
Maximum Likelihood (ML) decoding of forward error correction codes is known to be optimally accurate, but is not used in practice as it proves too challenging to efficiently implement. Here we introduce a ML decoder called SGRAND, which is…
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)…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
In this work, we investigate guessing random additive noise decoding (GRAND) with quantized soft input. First, we analyze the achievable rate of ordered reliability bits GRAND (ORBGRAND), which uses the rank order of the reliability as…
The ordered-reliability bits (ORB) variant of guessing random additive noise decoding (GRAND), known as ORBGRAND, achieves remarkably low time complexity at high code rates compared to other GRAND variants. However, its computational…
Ultra-reliable low-latency communication (URLLC), a major 5G New-Radio use case, is the key enabler for applications with strict reliability and latency requirements. These applications necessitate the use of short-length and high-rate…
In this paper, we distinguish two guessing algorithms for decoding binary linear codes. One is the guessing noise decoding (GND) algorithm, and the other is the guessing codeword decoding (GCD) algorithm. We prove that the GCD is a maximum…
We establish that it is possible to extract accurate blockwise and bitwise soft output from Guessing Codeword Decoding with minimal additional computational complexity by considering it as a variant of Guessing Random Additive Noise…
This paper considers a transmitter, which uses random linear coding (RLC) to encode data packets. The generated coded packets are broadcast to one or more receivers. A receiver can recover the data packets if it gathers a sufficient number…