Related papers: Applications of Convolutional Codes to DNA Codes a…
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the…
We study permutations over the set of $\ell$-grams, that are feasible in the sense that there is a sequence whose $\ell$-gram frequency has the same ranking as the permutation. Codes, which are sets of feasible permutations, protect…
The decoding of error syndromes of surface codes with classical algorithms may slow down quantum computation. To overcome this problem it is possible to implement decoding algorithms based on artificial neural networks. This work reports a…
Several technological applications require the translation of a protein into a nucleic acid that codes for it (``backtranslation''). The degeneracy of the genetic code makes this translation ambiguous; moreover, not every translation is…
We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use…
In this paper, we study error exponents for a concatataned coding based class of DNA storage codes in which the number of reads performed can be variable. That is, the decoder can sequentially perform reads and choose whether to output the…
In this paper, convolutional network coding is formulated by means of matrix power series representation of the local encoding kernel (LEK) matrices and global encoding kernel (GEK) matrices to establish its theoretical fundamentals for…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
We describe a strategy for constructing codes for DNA-based information storage by serial composition of weighted finite-state transducers. The resulting state machines can integrate correction of substitution errors; synchronization by…
Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a precoding step before the polar transform. In this scheme, the polar transform (as a mapper) and the…
DNA Data storage has recently attracted much attention due to its durable preservation and extremely high information density (bits per gram) properties. In this work, we propose a hybrid coding strategy comprising of generalized…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
Constrained sequence (CS) codes, including fixed-length CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy…
Algorithms that use Large Language Models (LLMs) to evolve code arrived on the Genetic Programming (GP) scene very recently. We present LLM GP, a formalized LLM-based evolutionary algorithm designed to evolve code. Like GP, it uses…
This paper characterizes the inherent power of evolutionary algorithms. This power depends on the computational properties of the genetic encoding. With some encodings, two parents recombined with a simple crossover operator can sample from…
Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are…
In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and…
Codes have been used for centuries to convey secret information.To a cryptanalyst, the interception of a code is only the first step in recovering a secret message.Deoxyribonucleic acid (DNA) is a biological and molecular code.Through the…
Quantum convolutional coding is a technique for encoding a stream of quantum information before transmitting it over a noisy quantum channel. Two important goals in the design of quantum convolutional encoders are to minimize the memory…
DNA based storage systems received attention by many researchers. This includes archival and re-writable random access DNA based storage systems. In this work, we have developed an efficient technique to encode the data into DNA sequence by…