  DNA, with remarkable properties of high density, durability, and
replicability, is one of the most appealing storage media. Emerging DNA storage
technologies use composite DNA letters, where information is represented by
probability vectors, leading to higher information density and lower
synthesizing costs than regular DNA letters. However, it faces the problem of
inevitable noise and information corruption. This paper explores the channel of
composite DNA letters in DNA-based storage systems and introduces block codes
for limited-magnitude probability errors on probability vectors. First, outer
and inner bounds for limited-magnitude probability error correction codes are
provided. Moreover, code constructions are proposed where the number of errors
is bounded by t, the error magnitudes are bounded by l, and the probability
resolution is fixed as k. These constructions focus on leveraging the
properties of limited-magnitude probability errors in DNA-based storage
systems, leading to improved performance in terms of complexity and redundancy.
In addition, the asymptotic optimality for one of the proposed constructions is
established. Finally, systematic codes based on one of the proposed
constructions are presented, which enable efficient information extraction for
practical implementation.
