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As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…
We show that for all $\varepsilon>0$, for sufficiently large $q\in\mathbb{N}$ power of $2$, for all $\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least…
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
Characterizing the distribution of high-dimensional statistical estimators is a challenging task, due to the breakdown of classical asymptotic theory in high dimension. This paper makes progress towards this by developing non-asymptotic…
We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…
The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress…
This paper proposes $\mathbf{C}$ommunication efficient $\mathbf{RE}$cursive $\mathbf{D}$istributed estimati$\mathbf{O}$n algorithm, $\mathcal{CREDO}$, for networked multi-worker setups without a central master node. $\mathcal{CREDO}$ is…
A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is proposed, referred to as tree-based Chase-type algorithm}. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns,…
We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these exponents can be written as simple optimizations over the R\'enyi…
Error-correcting codes are one of the most fundamental objects in pseudorandomness, with applications in communication, complexity theory, and beyond. Codes are useful because of their ability to support decoding, which is the task of…
We develop new list decoding algorithms for Tanner codes and distance-amplified codes based on bipartite spectral expanders. We show that proofs exhibiting lower bounds on the minimum distance of these codes can be used as certificates…
The exact order of the optimal sub-exponentially decaying factor in the classical bounds on the error probability of fixed-length codes over a Gallager-symmetric discrete memoryless channel with and without ideal feedback is determined.…
While the deep learning techniques promote the rapid development of the speech enhancement (SE) community, most schemes only pursue the performance in a black-box manner and lack adequate model interpretability. Inspired by Taylor's…
A Lagrange-dual (Gallager-style) lower bound is derived for the error exponent function of the typical random code (TRC) pertaining to the i.i.d. random coding ensemble and mismatched stochastic likelihood decoding. While the original…
We investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum system.…
Based on the principles of information theory, measure theory, and theoretical computer science, we introduce a signal deconvolution method with a wide range of applications to coding theory, particularly in zero-knowledge one-way…
Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and…
Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average…
Scaling laws aim to accurately predict model performance across different scales. Existing scaling-law studies almost exclusively rely on cross-entropy as the evaluation metric. However, cross-entropy provides only a partial view of…
This paper presents the use of non-autoregressive (NAR) approaches for joint automatic speech recognition (ASR) and spoken language understanding (SLU) tasks. The proposed NAR systems employ a Conformer encoder that applies connectionist…