Related papers: Design and Analysis of LT Codes with Decreasing Ri…
Coding for distributed computing supports low-latency computation by relieving the burden of straggling workers. While most existing works assume a simple master-worker model, we consider a hierarchical computational structure consisting of…
Learning, prediction, and compression are intimately connected: a model that accurately predicts the next symbol in a sequence can be coupled with a source coder to compress that sequence near its information-theoretic limit. When tokenized…
Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
Run-Length Encoding (RLE) is one of the most fundamental tools in data compression. However, its compression power drops significantly if there lacks consecutive elements in the sequence. In extreme cases, the output of the encoder may…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
Practical random network coding based schemes for multicast include a header in each packet that records the transformation between the sources and the terminal. The header introduces an overhead that can be significant in certain…
Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies…
Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets…
Large Language Models (LLMs) have recently made significant advances in code generation through the 'Chain-of-Thought' prompting technique. This technique empowers the model to autonomously devise "solution plans" to tackle intricate…
This paper introduces a new scheme of LT codes, named multiple configurations. In multiple configurations LT codes (MC-LT codes), multiple sets of output symbols are simultaneously provided to receivers for recovering the source data. Each…
We focus on the design of distributed Luby transform (DLT) codes for erasure networks with multiple sources and multiple relays, communicating to a single destination. The erasure-floor performance of DLT codes improves with the maximum…
We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to…
Video compression systems must support increasing bandwidth and data throughput at low cost and power, and can be limited by entropy coding bottlenecks. Efficiency can be greatly improved by parallelizing coding, which can be done at much…
Reasoning is critical for large language models (LLMs) to excel in a wide range of tasks. While methods like Chain-of-Thought (CoT) reasoning and enhance LLM performance by decomposing problems into intermediate steps, they also incur…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
As one of their many applications, large language models (LLMs) have recently shown promise in automating register transfer level (RTL) code generation. However, conventional LLM decoding strategies, originally designed for natural…
This paper explores the design of convolutional codes for varying constraint lengths, focusing on their role in error correction in digital communication systems. Convolutional codes are essential in achieving reliable data transmission…
How can small-scale large language models (LLMs) efficiently utilize the supervision of LLMs to improve their generative quality? This question has been well studied in scenarios where there is no restriction on the number of LLM…