相关论文: Statistical Mechanics and Capacity-Approaching Err…

The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…

Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible…

Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…

Sparse Regression Codes (SPARCs) are capacity-achieving codes introduced for communication over the Additive White Gaussian Noise (AWGN) channels and were later extended to general memoryless channels. In particular it was shown via…

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…

Quantum metrology has been making amazing progress in the past decades. It is always in researchers' interest to search for new optimal states that improve parameter estimation. In this paper, we point out a connection between the code's…

The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…

The Consultative Committee for Space Data Systems (CCSDS) 141.11-O-1 Line Product Code (LPC) provides a rare opportunity to compare maximum-likelihood decoding and message passing. The LPC considered in this paper is intended to serve as…

An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…

It is well-known in the field of lossless data compression that probabilistic next-symbol prediction can be used to compress sequences of symbols. Deep neural networks are able to capture rich dependencies in data, offering a powerful means…

Recently, a new class of error-control codes, the polar codes, have attracted much attention. The polar codes are the first known class of capacity-achieving codes for many important communication channels. In addition, polar codes have…

We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…

We discuss the metastate, a probability measure on thermodynamic states, and its usefulness in addressing difficult questions pertaining to the statistical mechanics of systems with quenched disorder, in particular short-range spin glasses.…

Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…

For the additive Gaussian noise channel with average codeword power constraint, sparse superposition codes and adaptive successive decoding is developed. Codewords are linear combinations of subsets of vectors, with the message indexed by…

Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel…

Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying…

Neural metrics have achieved impressive correlation with human judgements in the evaluation of machine translation systems, but before we can safely optimise towards such metrics, we should be aware of (and ideally eliminate) biases toward…

We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…

Spatially-coupled (SC) codes are a class of low-density parity-check (LDPC) codes that have excellent performance thanks to the degrees of freedom they offer. An SC code is designed by partitioning a base matrix into components, the number…