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: Alice has a sequence $\bx$ of length $n$. Bob wishes to guess $\bx$, yet he is satisfied with finding any sequence $\hat{\bx}$ which is within a given distortion $D$ from $\bx$. Thus, he successively submits queries to Alice, until receiving an affirmative answer, stating that his guess was within the required distortion. Finding guessing strategies which minimize the number of guesses (the \emph{guesswork}), and analyzing its properties (e.g., its $\rho$--th moment) has several applications in information security, source and channel coding. Guessing subject to a distortion constraint is especially useful when considering contemporary biometrically--secured systems, where the "password" which protects the data is not a single, fixed vector but rather a \emph{ball of feature vectors} centered at some $\bx$, and any feature vector within the ball results in acceptance. We formally define the guessing problem under distortion in \emph{four different setups}: memoryless sources, guessing through a noisy channel, sources with memory and individual sequences. We suggest a randomized guessing strategy which is asymptotically optimal for all setups and is \emph{five--fold universal}, as it is independent of the source statistics, the channel, the moment to be optimized, the distortion measure and the distortion level.
翻译:在本文中, 我们考虑在扭曲限制下猜测序列的问题 。 具体地说, 我们假设爱丽丝和鲍勃之间的游戏: 爱丽丝有一个序列 $\ bx$, 长度为 美元。 鲍勃想要猜测$\ bx$, 但是他满足于从$\ bx$ 找到任何序列 $\ hat xx} 美元, 这在特定扭曲范围内 $\ bx$ 。 因此, 他接连向爱丽丝提出询问, 直至得到肯定的答复, 声明他的猜测在所需的扭曲范围之内。 找到可以将猜数( emph{ guesswork} 数目减少到最小值数( $\ bx{ guesswork} 的策略 。 在信息安全、 来源和渠道中, 测量一个扭曲值不是单一的、 固定的矢量 。 测量数据不是单一的矢量, 以某位的源数( ) 以及球内的任何特性矢量( 例如, road_ ) 的源( ) ) 正式地) 、 表示一个不同的记忆的源( 我们的排序 、 将一个不同的源) 、 和整个的顺序 定义一个不同的记忆的 。