Related papers: Guessing random additive noise decoding with symbo…
We propose a general framework for decoding quantum error-correcting codes with generative modeling. The model utilizes autoregressive neural networks, specifically Transformers, to learn the joint probability of logical operators and…
In this work we develop the maximum likelihood detection (MLD) algorithm for noncoherent amplitude shift keying (NCASK) systems in additive white Gaussian noise (AWGN) channels. The developed algorithm was used to investigate the…
Large language models (LLMs) have shown remarkable capabilities in code generation. However, the effects of hallucinations (e.g., output noise) make it particularly challenging for LLMs to generate high-quality code in one pass. In this…
We present a family of additive quantum error-correcting codes whose capacities exceeds that of quantum random coding (hashing) for very noisy channels. These codes provide non-zero capacity in a depolarizing channel for fidelity parameters…
We propose a novel soft-aided iterative decoding algorithm for product codes (PCs). The proposed algorithm, named iterative bounded distance decoding with combined reliability (iBDD-CR), enhances the conventional iterative bounded distance…
In this paper, we first present the asymptotic performance of serially concatenated low-density generator-matrix (SCLDGM) codes for binary input additive white Gaussian noise channels using discretized density evolution (DDE). We then…
This paper considers a general framework for massive random access based on sparse superposition coding. We provide guidelines for the code design and propose the use of constant-weight codes in combination with a dictionary design based on…
For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall…
In this paper, we use reinforcement learning to find effective decoding strategies for binary linear codes. We start by reviewing several iterative decoding algorithms that involve a decision-making process at each step, including…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
A complexity-adaptive tree search algorithm is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive…
For the additive white Gaussian noise channel with average codeword power constraint, new coding methods are devised in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design,…
This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. The proposed method is applicable to various channels and ensembles. The focus is on both…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
Motivated by applications of biometric identification and content identification systems, we consider the problem of random coding for channels, where each codeword undergoes lossy compression (vector quantization), and where the decoder…
We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the 2D surface code with a noiseless syndrome extraction. First, we show how to implement MLD exactly in time…
This paper presents a new class of sparse superposition codes for low-rates and short-packet communications over the additive white Gaussian noise channel. The new code is orthogonal sparse superposition (OSS) code. A codeword of OSS codes…
Polar codes have been adopted as the control channel coding scheme in the fifth generation new radio (5G NR) standard due to its capacity-achievable property. Traditional polar decoding algorithms such as successive cancellation (SC) suffer…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…