Limited-Magnitude Error Correction for Probability Vectors in DNA Storage

DNA, with remarkable properties of high density and stability, particularly for long-term data archiving, is one of the most appealing storage media. Emerging DNA storage technologies use composite DNA letters, where information is represented by a probability vector, leading to higher information density and lower synthesizing cost than single DNA letters. However, it faces the problem of inevitable noise and information corruption. This paper studies the channel of composite DNA letters in DNA storage and block codes for symmetric limited-magnitude errors on probability vectors. We provide outer and inner bounds for limited-magnitude probability error correction codes. Moreover, we propose code constructions where the number of errors is bounded by l, the error magnitudes are bounded by l, and the probability resolution is fixed as k. Our constructions exploit the properties of the limited-magnitude errors, and improve the performance in terms of complexity and redundancy.