19 papers · ranked by Valyu relevance
Yixin Wang, Tingting Zhu, Xiao Ma
We propose in this paper to exploit convolutional low density generator matrix (LDGM) codes for transmission of Bernoulli sources over binary-input output-symmetric (BIOS) channels. To this end, we present a new framework to prove the coding theorems for linear codes, which unifies the channel coding theorem, the…
Xiangping Zheng, Xiao Ma
In this paper, we prove that the sub-field images of generalized Reed-Solomon (RS) codes can achieve the symmetric capacity of p-ary memoryless channels. Unlike the totally random linear code ensemble, as a class of maximum distance separable (MDS) codes, the generalized RS code ensemble lacks the pair-wise…
Shuichi Hirahara, Zhenjian Lu, Mikito Nanashima
The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to obtaining fundamental results in average-case complexity, yet whether any…
Jesús E. Garca, Verónica A. González-López, Gustavo H. Tasca, Karina Y. Yaginuma + 1 more
In the framework of coding theory, under the assumption of a Markov process $(X_{t})$ on a finite alphabet $A,$ the compressed representation of the data will be composed of a description of the model used to code the data and the encoded data. Given the model, the Huffman’s algorithm is optimal for the number of bits…
Rui Tang, Songjie Xie, Youlong Wu, Song-Nam Hong
This paper focuses on K-receiver discrete-time memoryless broadcast channels (DM-BCs) with private messages, where the transmitter wishes to convey K private messages to K receivers. A general inner bound on the capacity region is proposed based on an exhaustive message splitting and a K-level modified Marton’s coding.…
Maximilian Gehri, Lukas Stelzl, Heinz Koeppl
Biochemical systems process signals through stochastic reaction dynamics that are inherently continuous in time and often exhibit memory, feedback, and nonequilibrium driving. At the same time, they are frequently modeled by effective reactions, e.g., multi-step processes such as transcription are treated as single…
Henk D. L. Hollmann, Patrick Solé
We construct a family of linear optimal functional-repair regenerating storage codes with parameters $({m,(n,k),(r,α,β)}={(2r-α+1)α/2,(r+1,r),(r,α,1)})$ for any integers $r,α$ with $1\leqα\leqr$, over any field when $α\in{1,r-1,r}$, and over any finite field $F_{q}$ with $q\geqr-1$ otherwise. These storage codes are…
Valéria G. Pedrosa, Max H. M. Costa, Sangun Park
The index coding problem consists of a system with a server and multiple receivers with different side information and demand sets, connected by a noiseless broadcast channel. The server knows the side information available to the receivers. The objective is to design an encoding scheme that enables all receivers to…
Spencer Congero, K. Zeger
For any finite discrete source, the competitive advantage of prefix code C1 over prefix code C2 is the probability C1 produces a shorter codeword than C2, minus the probability C2 produces a shorter codeword than C1. For any source, a prefix code is competitively optimal if it has a nonnegative competitive advantage…
Lihong Cao
The human brain encodes a virtually infinite repertoire of semantic concepts using a finite number of neurons, a feat that defies the capacity limits of classical attractor networks. While “Concept Cells” in the medial temporal lobe (MTL) exhibit extreme sparsity, the information-theoretic principles governing their…
Alix Petit, Aida Koch, Logan Lewis, Christian Schmidt + 1 more
'Adrain Vdberg'] Abstract: given the importance of the claim, we want to start by exposing the following consideration: this claim comes out more than a year after the article "Practical applications of Set Shaping Theory in Huffman coding" which reports the program that carried out an experiment of data compression in…
M. Ashok Kumar, Albert Sunny, Ashish Thakre, Ashisha Kumar + 3 more
'G. Dinesh Manohar' 'Nicusor Minculete' 'Shigeru Furuichi'] This paper establishes a close relationship among the four information theoretic problems, namely Campbell source coding, Arikan guessing, Huleihel et al. memoryless guessing and Bunte and Lapidoth tasks’ partitioning problems in the IID-lossless case. We…
Lei M. Li, Boris Ryabko
We consider the lossless compression bound of any individual data sequence. Conceptually, its Kolmogorov complexity is such a bound yet uncomputable. According to Shannon’s source coding theorem, the average compression bound is $nH$, where n is the number of words and H is the entropy of an oracle probability…
Fatih Dinc, Marta Blanco-Pozo, David Klindt, Francisco Acosta + 8 more
Many neural recordings have revealed low-dimensional sets of behaviorally relevant variables encoded within large-scale neural activity patterns. However, dimensionality reduction analyses alone cannot yield causal explanations for how networks stably implement computations that are resilient to the substantial…
Hongyang Liu, Wei Yan
For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this interval, the optimal code length for the symbol equals $k$. Furthermore, for infinite…
Michael Yarus
The Standard Genetic Code (SGC) can arise by fusion of partial codes evolved in different individuals, perhaps for differing prior tasks. Such code fragments can be unified into an SGC after late evolution of accurate third-position Crick wobble. Late wobble advent fills in the coding table, leaving only later…
Kun Tu, Dariusz Puchala, Jun Chen, Sadaf Salehkalaibar
In this paper, we address the problem of m-gram entropy variable-to-variable coding, extending the classical Huffman algorithm to the case of coding m-element (i.e., m-grams) sequences of symbols taken from the stream of input data for $m>1$. We propose a procedure to enable the determination of the frequencies of the…
Miloje Rakočević
In some previous works (2018a,b; 2019, 2021a,b, 2022) we presented a new type of mirror symmetry, expressed in the set of protein amino acids; such a symmetry, that it simultaneously represents the semiotic essence of the genetic code. In this paper we provide new evidences that the genetic code represents the unity of…
Fajia Sun, Long Qian
DNA has been pursued as a compelling medium for digital data storage during the past decade. While large-scale data storage and random access have been achieved in artificial DNA, the synthesis cost keeps hindering DNA data storage from popularizing into daily life. In this study, we proposed a more efficient paradigm…