Related papers: Analysis and Practice of Uniquely Decodable One-to…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
The notion of universally decodable matrices (UDMs) was recently introduced by Tavildar and Viswanath while studying slow fading channels. It turns out that the problem of constructing UDMs is tightly connected to the problem of…
In this paper we give several new constructions of WOM codes. The novelty in our constructions is the use of the so called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction…
Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
Two sets $A, B \subseteq \{0, 1\}^n$ form a Uniquely Decodable Code Pair (UDCP) if every pair $a \in A$, $b \in B$ yields a distinct sum $a+b$, where the addition is over $\mathbb{Z}^n$. We show that every UDCP $A, B$, with $|A| =…
The problem of joint universal source coding and identification is considered in the setting of fixed-rate lossy coding of continuous-alphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any…
This paper proposes an algorithm to search a family of multiple sets of minimum correlated one dimensional uni-polar (optical) orthogonal codes (1-DUOC) or optical orthogonal codes (OOC) with fixed as well as variable code parameters. The…
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 basic problem for constant dimension codes is to determine the maximum possible size $A_q(n,d;k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$, called codewords, such that the subspace distance satisfies…
In this paper, we propose the use of a deterministic sequence, known as unique word (UW), instead of the cyclic prefix (CP) in generalized frequency division multiplexing (GFDM) systems. The UW consists of known sequences that, if not null,…
In this paper, we propose \textbf{UniCode}, a novel approach within the domain of multimodal large language models (MLLMs) that learns a unified codebook to efficiently tokenize visual, text, and potentially other types of signals. This…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…
This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…
Mutually Uncorrelated (MU) codes are a class of codes in which no proper prefix of one codeword is a suffix of another codeword. These codes were originally studied for synchronization purposes and recently, Yazdi et al. showed their…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
We consider uniquely-decodable coding for zero-error network function computation, where in a directed acyclic graph, the single sink node is required to compute with zero error a target function multiple times, whose arguments are the…
An asynchronous $\ka$-active-user unsourced multiple access channel (AUMAC) is a key model for uncoordinated massive access in future networks. We focus on a scenario where each transmission is subject to the maximal delay constraint…
It is well known that Space-Time Block Codes (STBCs) from orthogonal designs (ODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes…
Universally decodable matrices (UDMs) can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers $L$ and $N$ and a prime power $q$. The main result of this paper is…