Related papers: Hamming Code for Multiple Sources
We are interested in how to best communicate a real valued source to a number of destinations (sinks) over a network with capacity constraints in a collective fidelity metric over all the sinks, a problem which we call joint network-source…
We define generalized Hamming weights for almost affine codes. We show how various aspects and applications of generalized Hamming weights for linear codes, such as Wei duality, generalized Kung's bound, profiles, connection to wire-tap…
In this paper we propose a revisitation of the topic of unique decodability and of some fundamental theorems of lossless coding. It is widely believed that, for any discrete source X, every "uniquely decodable" block code satisfies E[l(X_1…
Stopping sets, and in particular their numbers and sizes, play an important role in determining the performance of iterative decoders of linear codes over binary erasure channels. In the 2004 Shannon Lecture, McEliece presented an…
We consider the variable-to-fixed length lossy source coding (VFSC) problem. The optimal compression rate of the average length of variable-to-fixed source coding, allowing a non-vanishing probability of excess-distortion $\varepsilon$, is…
Training and serving Large Language Models (LLMs) relies heavily on parallelization and collective operations, which are frequently bottlenecked by network bandwidth. Lossless compression using e.g., Huffman codes can alleviate the issue,…
A general method of coding over expansion is proposed,which allows one to reduce the highly non-trivial problems of coding over analog channels and compressing analog sources to a set of much simpler subproblems, coding over discrete…
A multiterminal lossy coding problem, which includes various problems such as the Wyner-Ziv problem and the complementary delivery problem as special cases, is considered. It is shown that any point in the achievable rate-distortion region…
We are interested in how to best communicate a (usually real valued) source to a number of destinations (sinks) over a network with capacity constraints in a collective fidelity metric over all the sinks, a problem which we call joint…
A weighted Hamming metric is introduced in [4] and it showed that the binary generalized Goppa code is a perfect code in some weighted Hamming metric. In this paper, we study the weight structures which admit the binary Hamming code and the…
Symmetrical Multilevel Diversity Coding (SMDC) is a network compression problem introduced by Roche (1992) and Yeung (1995). In this setting, a simple separate coding strategy known as superposition coding was shown to be optimal in terms…
An intuitive outer bound for the multiterminal source coding problem is given. The proposed bound explicitly couples the rate distortion functions for each source and correlation measures which derive from a "strong" data processing…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
This paper investigates the problem of zero-delay joint source-channel coding of a vector Gauss-Markov source over a multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) channel with feedback. In contrast to the…
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…
Spatial computing architectures promise a major stride in performance and energy efficiency over the traditional load/store devices currently employed in large scale computing systems. The adoption of high-level synthesis (HLS) from…
Many applications require data processing to be performed on individual pieces of data which are of finite sizes, e.g., files in cloud storage units and packets in data networks. However, traditional universal compression solutions would…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
Homophonic coding is a framework to reversibly convert a message into a sequence with some target distribution. This is a promising tool to generate a codeword with a biased code-symbol distribution, which is required for capacity-achieving…
In this paper we consider lossless source coding for a class of sources specified by the total variational distance ball centred at a fixed nominal probability distribution. The objective is to find a minimax average length source code,…