Related papers: A Refinement of Expurgation
Randomness extraction is the process of constructing a source of randomness of high quality from one or several sources of randomness of lower quality. The problem can be modeled using probability distributions and min-entropy to measure…
This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can…
A remarkable conjecture of Feige (2006) asserts that for any collection of $n$ independent non-negative random variables $X_1, X_2, \dots, X_n$, each with expectation at most $1$, $$ \mathbb{P}(X < \mathbb{E}[X] + 1) \geq \frac{1}{e}, $$…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
This paper studies multiuser random coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, an error exponent is obtained that is tight with…
Describes a near-linear-time algorithm for a variant of Huffman coding, in which the letters may have non-uniform lengths (as in Morse code), but with the restriction that each word to be encoded has equal probability. [See also ``Huffman…
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…
Communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding is considered. The average bit error probability of an irregular LDPC code ensemble after a fixed number of…
The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
We derive the optimal exponent of the error probability of the quantum fixed-length pure state source coding in both cases of blind coding and visible coding. The optimal exponent is universally attained by Jozsa et al. (PRL, 81, 1714…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
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…
We consider the secret key generation problem when sources are randomly excited by the sender and there is a noiseless public discussion channel. Our setting is thus similar to recent works on channels with action-dependent states where the…
In this paper the ensemble of codes formed by a serial concatenation of a repetition code with multiple accumulators connected through random interleavers is considered. Based on finite length weight enumerators for these codes, asymptotic…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Probabilistic programming languages are valuable because they allow domain experts to express probabilistic models and inference algorithms without worrying about irrelevant details. However, for decades there remained an important and…
Most expressivity results for transformers treat them as language recognizers -- devices that accept or reject strings -- rather than as they are used in practice: as language models that generate strings autoregressively and…
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our…