  In the Levenshtein's sequence reconstruction problem a codeword is
transmitted through $N$ channels and in each channel a set of errors is
introduced to the transmitted word. In previous works, the restriction that
each channel provides a unique output word has been essential. In this work, we
assume only that each channel introduces a unique set of errors to the
transmitted word and hence some output words can also be identical. As we will
discuss, this interpretation is both natural and useful for deletion and
insertion errors. We give properties, techniques and (optimal) results for this
situation.
  Quaternary alphabets are relevant due to applications related to
DNA-memories. Hence, we introduce an efficient Las Vegas style decoding
algorithm for simultaneous insertion, deletion and substitution errors in
$q$-ary Hamming spaces for $q \geq 4$.
