18 papers · ranked by Valyu relevance
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…
Roberto Bruno, Roberto De Prisco, Ugo Vaccaro
This comprehensive survey examines the field of alphabetic codes, tracing their development from the 1960s to the present day. We explore classical alphabetic codes and their variants, analyzing their properties and the underlying mathematical and algorithmic principles. The paper covers the fundamental relationship…
Katharina Mir, Klaus Neuhaus, Martin Bossert, Steffen Schober + 1 more
'Eshel Ben-Jacob'] We consider the design and evaluation of short barcodes, with a length between six and eight nucleotides, used for parallel sequencing on platforms where substitution errors dominate. Such codes should have not only good error correction properties but also the code words should fulfil certain…
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…
Ezequiel López-Rubio
The reflected binary Gray code arranges the fixed-length binary representations of the integers so that consecutive numbers differ in a single bit. Its usefulness, however, is tied to a fixed word length $b$, which both caps the range of representable numbers at $2^{b}-1$ and wastes bits on small integers. We introduce…
Stephan Rafler
A code is presented for fast, easy and efficient communication over channels that allow only two signal types: a single sound (e.g. a knock), or no sound (i.e. silence). This is a true binary code while Morse code is a ternary code and does not work in such situations. Thus the presented code is more universal than…
Marco Baldi, Giacomo Ricciutelli, Nicola Maturo, Franco Chiaraluce
—In this work we study the reliability and secrecy performance achievable by practical low-density parity-check (LDPC) codes over the Gaussian wiretap channel. While several works have already addressed this problem in asymptotic conditions, i.e., under the hypothesis of codewords of infinite length, only a few…
Kees Schouhamer Immink, Jos H. Weber, Tuan Thanh Nguyen, Kui Cai + 2 more
The design of low-complexity and efficient constrained codes has been a major research item for many years. This paper reports on a versatile method named concatenated constrained codes for designing efficient fixed-length constrained codes with small complexity. A concatenated constrained code comprises two (or more)…
Krishnamurthy Kirthi, Subhash Kak
A universal code maps positive integers which represent the source messages into codewords of different lengths. The codeword elements are a set of digits that are constructed according to a specified rule, and they may be binary. There are various universal codes including the Elias codes, the Fibonacci universal…
Om Prakash, Ashutosh Singh, Ram Krishna Verma, Patrick Solé + 2 more
'Wei Cheng' 'Pavel Kraikivski'] The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring $(R:=F_{4}[v]/〈v3〉)$. We show an association between the codons and the…
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…
Ahmed Hareedy, Beyza Dabak, Robert Calderbank
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage devices, and in increasing the reliability of data transmission over wires. Over…
Azat Akhmetov, Andrew D. Ellington, Edward M. Marcotte
Encoding arbitrary digital information in DNA has attracted attention as a potential avenue for large scale and long term data storage. However, in order to enable DNA data storage technologies there needs to be improvements in data storage fidelity (tolerance to mutation), the facility of writing and reading the data…
Kuba Nowak, Paweł Błażej, Małgorzata Wnetrzak, Dorota Mackiewicz + 1 more
Reprogramming of the standard genetic code in order to include non-canonical amino acids (ncAAs) opens a new perspective in medicine, industry and biotechnology. There are several methods of engineering the code, which allow us for storing new genetic information in DNA sequences and transmitting it into the protein…
W. Jeffrey Johnston, Stephanie E. Palmer, David J. Freedman, Stefano Fusi
'Stefano Fusi'] Neuronal activity in the brain is variable, yet both perception and behavior are generally reliable. How does the brain achieve this? Here, we show that the conjunctive coding of multiple stimulus features, commonly known as nonlinear mixed selectivity, may be used by the brain to support reliable…
Andrzej Chmielowiec, Paweł Litwin, Philip Broadbridge, Raúl Alcaraz
This article deals with compression of binary sequences with a given number of ones, which can also be considered as a list of indexes of a given length. The first part of the article shows that the entropy H of random n-element binary sequences with exactly k elements equal one satisfies the inequalities…
Paweł Błażej, Dariusz R. Kowalski, Dorota Mackiewicz, Małgorzata Wnetrzak + 2 more
The standard genetic code (SGC) is the set of rules by which genetic information is translated into proteins, from codons, i.e. triplets of nucleotides, to amino acids. The questions about the origin and the main factor responsible for the present structure of the code are still under a hot debate. Various…
John-Antonio Argyriadis, Yang-Hui He, Vishnu Jejjala, Djordje Minic
We study the dynamics of genetic code evolution. The algorithm of Vetsigian et al. [1] provides a solution that is both optimal and universal. We reproduce and analyze the algorithm as a dynamical system. All the parameters used in the model are varied to assess their impact on achieving universality. We show that by…