Related papers: The approximate maximum-likelihood certificate

LLMs enable qualitative coding at large scale, but assessing reliability remains challenging where human experts seldom agree. We investigate confidence-diversity calibration as a quality assessment framework for accessible coding tasks…

In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density parity-check (LDPC) codes. We first relax the maximum likelihood (ML) decoding problem to a LP problem by using check-node decomposition.…

Low-density parity-check (LPDC) decoders assume the channel estate information (CSI) is known and they have the true a posteriori probability (APP) for each transmitted bit. But in most cases of interest, the CSI needs to be estimated with…

This paper reviews the potential channel decoding techniques for ultra-reliable low-latency communications (URLLC). URLLC is renowned for its stringent requirements including ultra-reliability, low end-to-end transmission latency, and…

A single input multiple output (SIMO) multiple access channel, with a large number of transmitters sending symbols from a constellation to the receiver of a multi-antenna base station, is considered. The fundamental limits of joint decoding…

Large Language Models (LLMs) have shown remarkable progress in multiple-choice question answering (MCQA), but their inherent unreliability, such as hallucination and overconfidence, limits their application in high-risk domains. To address…

Index coded PSK modulation over an AWGN broadcast channel, for a given index coding problem (ICP) is studied. For a chosen index code and an arbitrary mapping (of broadcast vectors to PSK signal points), we have derived a decision rule for…

The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…

Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is appealing due to its low complexity, yet it often exhibits convergence issues due to quantum degeneracy and short cycles that exist in the Tanner graph.…

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…

In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…

Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…

Probabilistic relational models such as parametric factor graphs enable efficient (lifted) inference by exploiting the indistinguishability of objects. In lifted inference, a representative of indistinguishable objects is used for…

Approximate Bayesian Computation (ABC) is a popular computational method for likelihood-free Bayesian inference. The term "likelihood-free" refers to problems where the likelihood is intractable to compute or estimate directly, but where it…

In this paper upper and lower bounds on the probability of decoding failure under maximum likelihood decoding are derived for different (nonbinary) Raptor code constructions. In particular four different constructions are considered; (i)…

We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Programming (LP) at moderate and large Signal-to-Noise-Ratios (SNR). Utilizing a combination of the previously introduced pseudo-codeword-search…

A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as Approximate Bayesian Computation, build Monte Carlo samples of the…

Approximate Bayesian computation (ABC) is an approach for sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model,…

Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two…

A new method for low-complexity near-maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over the additive white Gaussian noise channel is presented. The proposed method termed belief-propagation--list erasure decoding…