Rates of DNA Sequence Profiles for Practical Values of Read Lengths

TL;DR

This paper analyzes the number of profile vectors in DNA data storage, providing exact values, bounds, and efficient algorithms for encoding and decoding, especially for practical read lengths and alphabet sizes.

Contribution

It offers new enumeration bounds and efficient algorithms for profile vectors in DNA storage, enhancing understanding of their practical application.

Findings

Number of profile vectors is at least $q^{ heta n}$ for certain parameters.

Provides exact enumeration and lower bounds on profile vectors.

Develops efficient encoding and decoding algorithms for specific profile vector families.

Abstract

A recent study by one of the authors has demonstrated the importance of profile vectors in DNA-based data storage. We provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size $q$, read length $\ell$, and word length $n$.Consequently, we demonstrate that for $q\ge 2$ and $n\le q^{\ell/2-1}$, the number of profile vectors is at least $q^{\kappa n}$ with $\kappa$ very close to one.In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for each of two particular families of profile vectors.