On the number of DNA sequence profiles for practical values of read lengths

A recent study by one of the authors has demonstrated the relevance 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 ℓ, and word length n. Consequently, we demonstrate that for q ≥ 3 and n = q
^a
ℓ, a = o(ℓ), the number of profile vectors is at least q
^κn
for some constant 0 < κ ≤ 1. In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for a family of profile vectors.