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We present a method for upper and lower bounding the right and the left tail probabilities of continuous random variables (RVs). For the right tail probability of RV $X$ with probability density function $f (x)$, this method requires first…

Variable length codes exhibit de-synchronization problems when transmitted over noisy channels. Trellis decoding techniques based on Maximum A Posteriori (MAP) estimators are often used to minimize the error rate on the estimated sequence.…

Long-tail recognition tackles the natural non-uniformly distributed data in real-world scenarios. While modern classifiers perform well on populated classes, its performance degrades significantly on tail classes. Humans, however, are less…

Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…

Probabilistic recurrence relations (PRRs) are a standard formalism for describing the runtime of a randomized algorithm. Given a PRR and a time limit $\kappa$, we consider the classical concept of tail probability $\Pr[T \ge \kappa]$, i.e.,…

Ensuring the safety of neural networks under input uncertainty is a fundamental challenge in safety-critical applications. This paper builds on and expands Fazlyab's quadratic-constraint (QC) and semidefinite-programming (SDP) framework for…

We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use…

We study a controlled partial-KV decoding setting in which exact unnormalized softmax contributions are computed for sink/tail anchors and a retrieved token set, while the remaining prefill tokens are represented by a residual estimate. We…

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…

Runtime analysis, as a branch of the theory of AI, studies how the number of iterations algorithms take before finding a solution (its runtime) depends on the design of the algorithm and the problem structure. Drift analysis is a…

We propose a new class of information-coupled (IC) Turbo codes to improve the transport block (TB) error rate performance for long-term evolution (LTE) systems, while keeping the hybrid automatic repeat request protocol and the Turbo…

We present an abstract framework for a posteriori error estimation for approximations of scalar parabolic evolution equations, based on elliptic reconstruction techniques [10, 9, 3, 5]. In addition to its original application (to derive…

Fine-tuning is the primary methodology for tailoring pre-trained large language models to specific tasks. As the model's scale and the diversity of tasks expand, parameter-efficient fine-tuning methods are of paramount importance. One of…

We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and…

We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…

In a previous work, the authors proposed a Grammatical Evolution algorithm to automatically generate Lindenmayer Systems which represent fractal curves with a pre-determined fractal dimension. This paper gives strong statistical evidence…

We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code…

The use of deep neural network for decoding error control code will encounter two problems, namely, the high-precision requirements of the error control code and the complexity of the neural network due to the long code. In this paper, a…

Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum convolutional codes are constructed from classical self-orthogonal $\F_4$-linear and $\F_2$-linear convolutional codes, respectively. These quantum convolutional…

Reinforcement Learning (RL) for Large Language Models (LLMs) faces a fundamental tension: the numerical divergence between high-throughput inference engines and numerically precise training engines. Although these systems share the same…