Related papers: On Linear Operator Channels over Finite Fields
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…
This paper examines the maximum code rate achievable by a data-driven communication system over some unknown discrete memoryless channel in the finite blocklength regime. A class of channel codes, called learning-based channel codes, is…
Linear operator broadcast channel (LOBC) models the scenario of multi-rate packet broadcasting over a network, when random network coding is applied. This paper presents the framework of algebraic coding for LOBCs and provides a…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
Recent research indicates that packet transmission employing random linear network coding can be regarded as transmitting subspaces over a linear operator channel (LOC). In this paper we propose the framework of linear operator broadcast…
In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…
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…
Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more efficient physical-layer network coding…
The problem of maximum rate achievable with analog network coding for a unicast communication over a layered wireless relay network with directed links is considered. A relay node performing analog network coding scales and forwards the…
In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding…
Network function computation is an active topic in network coding, with much recent progress for linear (over a finite field) computations over broadcast (LCBC) and multiple access (LCMAC) channels. Over a quantum multiple access channel…
We examine the issue of separation and code design for networks that operate over finite fields. We demonstrate that source-channel (or source-network) separation holds for several canonical network examples like the noisy multiple access…
We address the problem of optimizing the throughput of network coded traffic in mobile networks operating in challenging environments where connectivity is intermittent and locally available memory space is limited. Random linear network…
This paper investigates the performance of wireless systems that employ finite-blocklength channel codes for transmission and operate under queueing constraints in the form of limitations on buffer overflow probabilities. A block fading…
Network coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over…
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…
Random Linear Network Coding (RLNC) is a transmission scheme that opts for linear combinations of the transmitted packets at a subset of the intermediate nodes. This scheme is usually considered when Network Coding (NC) is desired over…
We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions (XOR). Formulated as a special vector linear code over GF($2$), an…