Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the Impact of a Single Edge on the Network Coding Capacity
243
0
0.0
(
0
)
Added by
Shirin Jalali
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this paper, we study the effect of a single link on the capacity of a network of error-free bit pipes. More precisely, we study the change in network capacity that results when we remove a single link of capacity $delta$. In a recent result, we proved that if all the sources are directly available to a single super-source node, then removing a link of capacity $delta$ cannot change the capacity region of the network by more than $delta$ in each dimension. In this paper, we extend this result to the case of multi-source, multi-sink networks for some special network topologies.
rate research
Read More
We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We establish an outer bound on the underlying secure capacity region of the index coding problem, which includes polymatroidal and security constraints, as well as the set of additional decoding constraints for legitimate receivers. We then propose a secure variant of the composite coding scheme, which yields an inner bound on the secure capacity region of the index coding problem. For the achievability of secure composite coding, a secret key with vanishingly small rate may be needed to ensure that each legitimate receiver who wants the same message as the eavesdropper, knows at least two more messages than the eavesdropper. For all securely feasible index coding problems with four or fewer messages, our numerical results establish the secure index coding capacity region.
The problem of network function computation over a directed acyclic network is investigated in this paper. In such a network, a sink node desires to compute with zero error a {em target function}, of which the inputs are generated at multiple source nodes. The edges in the network are assumed to be error-free and have limited capacity. The nodes in the network are assumed to have unbounded computing capability and be able to perform network coding. The {em computing rate} of a network code that can compute the target function over the network is the average number of times that the target function is computed with zero error for one use of the network. In this paper, we obtain an improved upper bound on the computing capacity, which is applicable to arbitrary target functions and arbitrary network topologies. This improved upper bound not only is an enhancement of the previous upper bounds but also is the first tight upper bound on the computing capacity for computing an arithmetic sum over a certain non-tree network, which has been widely studied in the literature. We also introduce a multi-dimensional array approach that facilitates evaluation of the improved upper bound. Furthermore, we apply this bound to the problem of computing a vector-linear function over a network. With this bound, we are able to not only enhance a previous result on computing a vector-linear function over a network but also simplify the proof significantly. Finally, we prove that for computing the binary maximum function over the reverse butterfly network, our improved upper bound is not achievable. This result establishes that in general our improved upper bound is non achievable, but whether it is asymptotically achievable or not remains open.
For a (single-source) multicast network, the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field. In this paper, we design a new class $mathcal{N}$ of multicast networks and obtain an explicit formula for the linear solvability of these networks, which involves the associated coset numbers of a multiplicative subgroup in a base field. The concise formula turns out to be the first that matches the topological structure of a multicast network and algebraic identities of a field other than size. It further facilitates us to unveil emph{infinitely many} new multicast networks linearly solvable over GF($q$) but not over GF($q$) with $q < q$, based on a subgroup order criterion. In particular, i) for every $kgeq 2$, an instance in $mathcal{N}$ can be found linearly solvable over GF($2^{2k}$) but emph{not} over GF($2^{2k+1}$), and ii) for arbitrary distinct primes $p$ and $p$, there are infinitely many $k$ and $k$ such that an instance in $mathcal{N}$ can be found linearly solvable over GF($p^k$) but emph{not} over GF($p^{k}$) with $p^k < p^{k}$. On the other hand, the construction of $mathcal{N}$ also leads to a new class of multicast networks with $Theta(q^2)$ nodes and $Theta(q^2)$ edges, where $q geq 5$ is the minimum field size for linear solvability of the network.
Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.
Cognitive radios have been studied recently as a means to utilize spectrum in a more efficient manner. This paper focuses on the fundamental limits of operation of a MIMO cognitive radio network with a single licensed user and a single cognitive user. The channel setting is equivalent to an interference channel with degraded message sets (with the cognitive user having access to the licensed users message). An achievable region and an outer bound is derived for such a network setting. It is shown that under certain conditions, the achievable region is optimal for a portion of the capacity region that includes sum capacity.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
