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The central problem in sequence reconstruction is to find the minimum number of distinct channel outputs required to uniquely reconstruct the transmitted sequence. According to Levenshtein’s work in 2001, this number is determined by the size of the maximum intersection between the error balls of any two distinct input sequences of the channel. In this work, we study the sequence reconstruction problem for the q-ary single-deletion single-substitution channel for any fixed integer q≥2.

In DNA sequencing, we often need to infer an unknown sequence from a collection of its corrupted copies. Each copy cannot faithfully tell the truth due to DNA fragmentation, point mutations, and measurement errors. The theoretical guarantee of unique reconstruction is thus of concern. This motivated the study of sequence reconstruction problems three decades ago. Recently, synthetic DNA has been regarded as an ultra-dense data storage medium. Sequence reconstruction is a crucial step in achieving reliable and efficient data readout.