The Levenshtein's Channel and the List Size in Information Retrieval

: Ville Junnila, Tero Laihonen, Tuomo Lehtilä

: IEEE International Symposium on Information Theory

: New York

: 2019

: IEEE International Symposium on Information Theory

: 2019 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)

: IEEE INT SYMP INFO

: IEEE International Symposium on Information Theory

: 295

: 299

: 5

: 978-1-5386-9291-2

DOI: https://doi.org/10.1109/ISIT.2019.8849616

The Levenshtein's channel model for substitution errors is relevant in information retrieval where information is received through many noisy channels. In each of the channels there can occur at most t errors and the decoder tries to recover the information with the aid of the channel outputs. Recently, Yaakobi and Bruck considered the problem where the decoder provides a list instead of a unique output. If the underlying code C subset of F-2(n) has error-correcting capability e, we write t = e vertical bar l, (l >= 1). In this paper, we provide new bounds on the size of the list. In particular, we give using the Sauer-Shelah lemma the upper bound l + 1 on the list size for large enough n provided that we have a sufficient number of channels. We also show that the bound l + 1 is the best possible.