相关论文: Zero-Error Sum Modulo Two with a Common Observatio…

The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…

A problem in zero-sum theory is to determine all pairs $(k,n)$ for which every minimal zero-sum sequence of length $k$ modulo $n$ has index $1$. While all other cases have been solved more than a decade ago, the case when $k$ equals $4$ and…

In this work, we propose a simple modification of the forward-backward splitting method for finding a zero in the sum of two monotone operators. Our method converges under the same assumptions as Tseng's forward-backward-forward method,…

We prove a lower estimate on the increase in entropy when two copies of a conditional random variable $X | Y$, with $X$ supported on $\mathbb{Z}_q=\{0,1,\dots,q-1\}$ for prime $q$, are summed modulo $q$. Specifically, given two i.i.d copies…

We consider the problem of distributed binary hypothesis testing of two sequences that are generated by an i.i.d. doubly-binary symmetric source. Each sequence is observed by a different terminal. The two hypotheses correspond to different…

We systematically investigate the complexity of counting subgraph patterns modulo fixed integers. For example, it is known that the parity of the number of $k$-matchings can be determined in polynomial time by a simple reduction to the…

The subset sum problem over finite fields is a well-known {\bf NP}-complete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a…

Vaidman pointed out the importance of modular values, and related the modular value of a Pauli spin operator to its weak value for specific coupling strengths [Phys. Rev. Lett. 105, 230401 (2010)]. It would be useful if this relationship is…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

This paper studies an almost-lossless source-channel coding scheme in which source messages are assigned to different classes and encoded with a channel code that depends on the class index. The code performance is analyzed by means of…

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…

We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less well-known imaging mechanism called modulo imaging, which can be used…

We investigate unification problems related to the Cipher Block Chaining (CBC) mode of encryption. We first model chaining in terms of a simple, convergent, rewrite system over a signature with two disjoint sorts: list and element. By…

In this work we study zero vs. epsilon-error capacity in network coding instances. For multicast network coding it is well known that all rates that can be delivered with arbitrarily small error probability can also be delivered with zero…

Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…

We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.

A coding problem for correlated information sources is investigated. Messages emitted from two correlated sources are jointly encoded, and delivered to two decoders. Each decoder has access to one of the two messages to enable it to…

We consider the function computation problem in a three node network with one encoder and two decoders. The encoder has access to two correlated sources $X$ and $Y$. The encoder encodes $X^n$ and $Y^n$ into a message which is given to two…

A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably)…

The doubling construction is a fast and important way to generate new solutions to the Hurwitz problem on sums of squares identities from any known ones. In this short note, we generalize the doubling construction and obtain from any given…