Related papers: Communication over Finite-Chain-Ring Matrix Channe…
Motivated by physical-layer network coding, this paper considers communication in multiplicative matrix channels over finite chain rings. Such channels are defined by the law $Y =A X$, where $X$ and $Y$ are the input and output matrices,…
This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…
In 2010, Silva, Kschischang and K\"otter studied certain classes of finite field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced. In this paper we consider a generalisation of…
This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The model considered here assumes…
Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its…
Messages in communication networks often are considered as "discrete" taking values in some finite alphabet (e.g. a finite field). However, if we want to consider for example communication based on analogue signals, we will have to consider…
The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…
The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a…
This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general -- indeed, it is…
Lattices possess elegant mathematical properties which have been previously used in the literature to show that structured codes can be efficient in a variety of communication scenarios, including coding for the additive white Gaussian…
The modeling and control of networks over finite lattices are studied via the algebraic state space approach. Using the semi-tensor product of matrices, we obtain the algebraic state space representation of the dynamics of (control)…
As the mobile application landscape expands, wireless networks are tasked with supporting various connection profiles, including real-time communications and delay-sensitive traffic. Among many ensuing engineering challenges is the need to…
In this paper we give the generalization of lifted codes over any finite chain ring. This has been done by using the construction of finite chain rings from $p$-adic fields. Further we propose a lattice construction from linear codes over…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
We fully determine the communication complexity of approximating matrix rank, over any finite field $\mathbb{F}$. We study the most general version of this problem, where $0\leq r<R\leq n$ are given integers, Alice and Bob's inputs are…
The Additive-Multiplicative Matrix Channel (AMMC) was introduced by Silva, Kschischang and K\"otter in 2010 to model data transmission using random linear network coding. The input and output of the channel are $n\times m$ matrices over a…
In this paper, we show that nested lattice codes achieve the capacity of arbitrary channels with or without non-casual state information at the transmitter. We also show that nested lattice codes are optimal for source coding with or…
As the mobile application landscape expands, wireless networks are tasked with supporting different connection profiles, including real-time traffic and delay-sensitive communications. Among many ensuing engineering challenges is the need…
In this paper, we consider the information-theoretic characterization of the set of achievable rates and distortions in a broad class of multiterminal communication scenarios with general continuous-valued sources and channels. A framework…
Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity $C$ and the…