## Abstract

In this paper, we consider the problem of guessing a sequence subject to a distortion constraint. Specifically,we assume the following game between Alice and Bob: Alicehas a sequence x of length *n*. Bob wishes to guess x, yethe is satisfied with finding any sequence xˆ which is withina given distortion *D* from *x*. Thus, he successively submitsqueries to Alice, until receiving an affirmative answer, stating thathis guess was within the required distortion. Finding guessingstrategies which minimize the number of guesses (the guesswork),and analyzing its properties (e.g., its *ρ*–th moment) has severalapplications in information security, source and channel coding.Guessing subject to a distortion constraint is especially usefulwhen considering contemporary biometrically–secured systems,where the “password” which protects the data is not a single,fixed vector but rather a ball of feature vectors centered at some x,and any feature vector within the ball results in acceptance.We formally define the guessing problem under distortion infour different setups: memoryless sources, guessing through anoisy channel, sources with memory and individual sequences.We suggest a randomized guessing strategy which is asymptotically optimal for all setups and is five–fold universal, as it isindependent of the source statistics, the channel, the moment tobe optimized, the distortion measure and the distortion level.

Original language | English |
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Pages (from-to) | 7714-7734 |

Journal | IEEE Transactions on Information Theory |

Volume | 68 |

Issue number | 12 |

DOIs | |

State | Published - 26 Jul 2022 |

## Keywords

- Guesswork
- asynchronous guessing
- rate-distortion theory
- universal distribution
- universal guessing

## ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences