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Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special…
In this paper we explore the decision regions of Linear Programming (LP) decoding. We compare the decision regions of an LP decoder, a Belief Propagation (BP) decoder and the optimal Maximum Likelihood (ML) decoder. We study the effect of…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Transformer models trained on long sequences often achieve higher accuracy than short sequences. Unfortunately, conventional transformers struggle with long sequence training due to the overwhelming computation and memory requirements.…
We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can hypothesis test between high-dimensional probability measures. These functions are a…
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…
With the success of transformer architectures across diverse applications, the error correction code transformer (ECCT) has gained significant attention for its superior decoding performance. In spite of its advantages, the error floor…
In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding…
Recent advancements in large language models (LLMs) have significantly improved code generation and program comprehension, accelerating the evolution of software engineering. Current methods primarily enhance model performance by leveraging…
Large language models (LLMs) exhibit impressive natural language capabilities but suffer from hallucination -- generating content ungrounded in the realities of training data. Recent work has focused on decoding techniques to improve…
This paper introduces a method to generate hierarchically modular networks with prescribed node degree list and proposes a metric to measure network modularity based on the notion of edge distance. The generated networks are used as test…
Large Language Models (LLMs) have become extremely potent instruments with exceptional capacities for comprehending and producing human-like text in a wide range of applications. However, the increasing size and complexity of LLMs present…
Label Distribution Learning (LDL) is a novel machine learning paradigm that assigns label distribution to each instance. Many LDL methods proposed to leverage label correlation in the learning process to solve the exponential-sized output…
Code LLMs have become extremely popular recently for modeling source code across a variety of tasks, such as generation, translation, and summarization. However, transformer-based models are limited in their capabilities to reason through…
We investigate the performance of rateless codes for single-server streaming to diverse users, assuming that diversity in users is present not only because they have different channel conditions, but also because they demand different…
In this paper, we investigate the problem of distributionally robust source coding, i.e., source coding under uncertainty in the source distribution, discussing both the coding and computational aspects of the problem. We propose two…
In-Context Learning (ICL) is an emergent capability of Large Language Models (LLMs). Only a few demonstrations enable LLMs to be used as blackbox for new tasks. Previous studies have shown that using LLMs' outputs as labels is effective in…
One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…
Detecting Large Language Model (LLM)-generated code is a growing challenge with implications for security, intellectual property, and academic integrity. We investigate the role of conditional probability distributions in improving…
In this letter, we evaluate the finite-length performance of network coding when using either random or structured encoding matrices. First, we present our novel construction of structured network codes over Fq (q = 2^m) using Pascal…