相关论文: Statistical mechanics of typical set decoding

In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi…

Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle…

The symbol error rate of the minimum distance detector for an arbitrary multi-dimensional constellation impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a non-negative power of…

Standard decoding strategies for text generation, including top-k, nucleus sampling, and contrastive search, select tokens based on likelihood, restricting selection to high-probability regions. Human language production operates…

We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…

Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…

We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits. Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner…

The problem of lossless fixed-rate streaming coding of discrete memoryless sources with side information at the decoder is studied. A random time-varying tree-code is used to sequentially bin strings and a Stack Algorithm with a variable…

We consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show…

A lattice decoder which represents messages explicitly as a mixture of Gaussians functions is given. In order to prevent the number of functions in a mixture from growing as the decoder iterations progress, a method for replacing N Gaussian…

The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…

A distributed lossy compression network with $L$ encoders and a decoder is considered. Each encoder observes a source and sends a compressed version to the decoder. The decoder produces a joint reconstruction of target signals with the mean…

We consider the topic of universal decoding with a decoder that does not have direct access to the codebook, but only to noisy versions of the various randomly generated codewords, a problem motivated by biometrical identification systems.…

Quantum stabilizer codes often struggle with syndrome errors due to measurement imperfections. Typically, multiple rounds of syndrome extraction are employed to ensure reliable error information. In this paper, we consider phenomenological…

We introduce a fault-tolerant protocol for code concatenation of a generalized Shor code using a butterfly network architecture with high noise thresholds and low ancilla overhead to allow implementation on current devices. We develop a…

Superposition codes are efficient for the Additive White Gaussian Noise channel. We provide here a replica analysis of the performances of these codes for large signals. We also consider a Bayesian Approximate Message Passing decoder based…

The lack of uniqueness arising by oversampling of Fourier coefficients is shown to provide a way of transmitting hidden information. A basic encoding/decoding system, developed on the basis of such a possibility, is discussed. The system is…

The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural…

Probabilistic Amplitude Shaping (PAS) is a coded-modulation scheme in which the encoder is a concatenation of a distribution matcher with a systematic Forward Error Correction (FEC) code. For reduced computational complexity the decoder can…

We discuss how subspace codes can be used to simultaneously correct errors and erasures when the network performs random linear network coding and the edges are noisy channels. This is done by combining the subspace code with a classical…