Related papers: Delay and Redundancy in Lossless Source Coding
Let C be a linear code with length n and minimum distance d. The stopping redundancy of C is defined as the minimum number of rows in a parity-check matrix for C such that the smallest stopping sets in the corresponding Tanner graph have…
[Draft] In this paper, the redundancy of Slepian Wolf coding is revisited. Applying the random binning and converse technique in \cite{yang}, the same results in \cite{he} are obtained with much simpler proofs. Moreover, our results reflect…
Exact queueing analysis of erasure networks with network coding in a finite buffer regime is an extremely hard problem due to the large number of states in the network. In such networks, packets are lost due to either link erasures or due…
We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued…
Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the…
Several systems possess the flexibility to serve requests in more than one way. For instance, a distributed storage system storing multiple replicas of the data can serve a request from any of the multiple servers that store the requested…
In this paper, we study the problem of latency and reliability trade-off in ultra-reliable low-latency communication (URLLC) in the presence of decoding complexity constraints. We consider linear block encoded codewords transmitted over a…
This paper investigates the error probability of several decoding methods for a source code with decoder side information, where the decoding methods are: 1) symbol-wise maximum a posteriori decoding, 2) successive-cancellation decoding,…
This document is written in order to establish a common base ground on which the majority of the relevant research about linear fountain codes can be analyzed and compared. As far as I am concerned, there is no unified approach that…
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…
We consider a novel variant of $d$-semifaithful lossy coding in which the distortion measure is revealed only to the encoder and only at run-time, as well as an extension of it in which the distortion constraint $d$ is also revealed at…
Source code is usually formatted with elements like indentation and newlines to improve readability for human developers. However, these visual aids do not seem to be beneficial for large language models (LLMs) in the same way since the…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
Bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types. Two achievable error exponents are derived based on partial decode-forward and compress-forward which are well-known…
Large Reasoning Models (LRMs) often suffer from overthinking, generating verbose reasoning traces that compromise both computational efficiency and interpretability. Unlike prior efforts that rely on global length-based rewards, we propose…
Consider a sequence $X^n$ of length $n$ emitted by a Discrete Memoryless Source (DMS) with unknown distribution $p_X$. The objective is to construct a lossless source code that maps $X^n$ to a sequence $\widehat{Y}^m$ of length $m$ that is…
For a given unconstrained dynamical system, input redundancy has been recently redefined as the existence of distinct inputs producing identical output for the same initial state. By directly referring to signals, this definition readily…
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that…
The problem of variable length and fixed-distortion universal source coding (or D-semifaithful source coding) for stationary and memoryless sources on countably infinite alphabets ($\infty$-alphabets) is addressed in this paper. The main…
Analog coding decouples the tasks of protecting against erasures and noise. For erasure correction, it creates an "analog redundancy" by means of band-limited discrete Fourier transform (DFT) interpolation, or more generally, by an…