Related papers: Design and Analysis of LT Codes with Decreasing Ri…
We analyze the second moment of the ripple size during the LT decoding process and prove that the standard deviation of the ripple size for an LT-code with length $k$ is of the order of $\sqrt k.$ Together with a result by Karp et. al…
Luby Transform (LT) code over finite field is a recent research topic. In order to find out the properties of LT codes over finite field, a novel degree distribution function is proposed in this paper. The main thinking of our developed…
We study improved degree distribution for Luby Transform (LT) codes which exhibits improved bit error rate performance particularly in low overhead regions. We construct the degree distribution by modifying Robust Soliton distribution. The…
This paper presents "Predictive Pipelined Decoding (PPD)," an approach that speeds up greedy decoding in Large Language Models (LLMs) while maintaining the exact same output as the original decoding. Unlike conventional strategies, PPD…
In this paper we analyze LT and Raptor codes under inactivation decoding. A first order analysis is introduced, which provides the expected number of inactivations for an LT code, as a function of the output distribution, the number of…
Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an…
To reduce computational complexity and delay in randomized network coded content distribution, and for some other practical reasons, coding is not performed simultaneously over all content blocks, but over much smaller, possibly overlapping…
In this work, we investigate a typical scenario in code generation where a developer edits existing code in real time and requests a code assistant, e.g., a large language model, to re-predict the next token or next line on the fly.…
Window decoding, first proposed to reduce decoding complexity for real-time decoding, is an essential component to realize scalable, universal-fault tolerant computation. Prior work has focused on improving throughput through…
Sparse random linear network coding (SRLNC) is an attractive technique proposed in the literature to reduce the decoding complexity of random linear network coding. Recognizing the fact that the existing SRLNC schemes are not efficient in…
Large language models have demonstrated exceptional capability in natural language understanding and generation. However, their generation speed is limited by the inherently sequential nature of their decoding process, posing challenges for…
Decoding strategies play a central role in shaping the reasoning ability of large language models (LLMs). Traditional methods such as greedy decoding and beam search often suffer from error propagation, while sampling-based approaches…
In this paper we analyze a specific class of rateless codes, called LT codes with unequal recovery time. These codes provide the option of prioritizing different segments of the transmitted data over other. The result is that segments are…
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…
This paper presents an efficient hardware design approach for list successive cancellation (LSC) decoding of polar codes. By applying path-overlapping scheme, the l instances of (l > 1) successive cancellation (SC) decoder for LSC with list…
Multidimensional Retiming is one of the most important optimization techniques to improve timing parameters of nested loops. It consists in exploring the iterative and recursive structures of loops to redistribute computation nodes on cycle…
Context: In the fast-paced evolution of software development, Large Language Models (LLMs) have become indispensable tools for tasks such as code generation, completion, analysis, and bug fixing. Ensuring the robustness of these models…
LT (Luby transform) codes are a celebrated family of rateless erasure codes (RECs). Most of existing LT codes were designed for applications in which a centralized encoder possesses all message blocks and is solely responsible for encoding…
We consider distributed Luby transform (DLT) codes for efficient packet transmission in a multi-way relay network, where the links are modeled as erasure channels. Density evolution is applied for asymptotic performance analysis, and…
In this work, we prove new results concerning the combinatorial properties of random linear codes. Firstly, we prove a lower bound on the list-size required for random linear codes over $\mathbb F_q$ $\varepsilon$-close to capacity to…