Related papers: The Birthday Problem and Zero-Error List Codes
For general memoryless systems, the typical information theoretic solution - when exists - has a "single-letter" form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme),…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error…
We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…
The aim of this work is to study the zero-error capacity of pure-state classical-quantum channels in the setting of list decoding. We provide an achievability bound for list-size two and a converse bound holding for every fixed list size.…
We probabilistically analyze the performance of the arithmetic coding algorithm under a probability model for binary data in which a message is received by a coder from a source emitting independent equally distributed bits, with 1…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
Vocabulary learning by children can be characterized by many biases. When encountering a new word, children as well as adults, are biased towards assuming that it means something totally different from the words that they already know. To…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is…
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…
Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory…
In an effort to develop the foundations for a non-stochastic theory of information, the notion of $\delta$-mutual information between uncertain variables is introduced as a generalization of Nair's non-stochastic information functional.…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
The problem of characterising the zero-error capacity region for multiple access channels even in the noiseless case has remained an open problem for over three decades. Motivated by this challenging question, a recently developed theory of…
In the marriage problem, a variant of the bi-parted matching problem, each member has a `wish-list' expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is…
A basic problem in information theory is the following: Let $\mathbf{P} = (\mathbf{X}, \mathbf{Y})$ be an arbitrary distribution where the marginals $\mathbf{X}$ and $\mathbf{Y}$ are (potentially) correlated. Let Alice and Bob be two…