Related papers: Statistical mechanics of typical set decoding
Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on…
We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
Consider binary linear codes obtained from bipartite graphs as follows. There are~\(k \geq 1\) left nodes each representing a message bit and there are~\(m = m(k)\) right nodes each representing a parity bit, generated from the…
A method is presented for investigating the periodic signal content of time series in which a number of signals is present, such as arising from the observation of multiperiodic oscillating stars in observational asteroseismology. Standard…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error…
We introduce a novel approach to error correction decoding in the presence of additive alpha-stable noise, which serves as a model of interference-limited wireless systems. In the absence of modifications to decoding algorithms, treating…
An efficient decoder is essential for quantum error correction, and data-driven neural decoders have emerged as promising, flexible solutions. Here, we introduce a diffusion model framework to infer logical errors from syndrome measurements…
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
Polar encoding, described by Arikan in IEEE Transactions on Information Theory, Vol. 55, No. 7, July 2009, was a milestone for telecommunications. A Polar code distributes information among high and low-capacity channels, showing the…
Noise is an important factor that influences the reliability of information acquisition, transmission, processing, and storage. In order to suppress the inevitable noise effects, a fault-tolerant information processing approach via quantum…
Low-density parity-check (LDPC) codes are specified by graphs, and are the error correction technique of choice in many communications and data storage contexts. Message passing decoders diffuse information carried by parity bits into the…
Gaussian noise induced by loss on Gaussian states may be corrected by distributing EPR entanglement through the loss channel, purifying the entanglement using a noiseless linear amplifier (NLA) and then using it for continuous-variable…
A majority logic decoder made of unreliable logic gates, whose failures are transient and datadependent, is analyzed. Based on a combinatorial representation of fault configurations a closed-form expression for the average bit error rate…
We present herein a scheme by which to accurately evaluate the error exponents of a lossy data compression problem, which characterize average probabilities over a code ensemble of compression failure and success above or below a critical…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
The quantum paradigm presents a phenomenon known as degeneracy that should improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse…
We explain an algorithm that approximately but efficiently assesses particular parity-check error-correcting codes of large, but finite, blocklength. This algorithm is based on the ``renormalization-group'' approach from physics: the idea…
The translation of written language has been known since the 3rd century BC; however, its necessity has become increasingly common in the information age. Today, many translators exist, based on encoder-decoder deep architectures,…