78 research outputs found
Algebraic Network Coding Approach to Deterministic Wireless Relay Networks
The deterministic wireless relay network model, introduced by Avestimehr et
al., has been proposed for approximating Gaussian relay networks. This model,
known as the ADT network model, takes into account the broadcast nature of
wireless medium and interference. Avestimehr et al. showed that the Min-cut
Max-flow theorem holds in the ADT network.
In this paper, we show that the ADT network model can be described within the
algebraic network coding framework introduced by Koetter and Medard. We prove
that the ADT network problem can be captured by a single matrix, called the
"system matrix". We show that the min-cut of an ADT network is the rank of the
system matrix; thus, eliminating the need to optimize over exponential number
of cuts between two nodes to compute the min-cut of an ADT network.
We extend the capacity characterization for ADT networks to a more general
set of connections. Our algebraic approach not only provides the Min-cut
Max-flow theorem for a single unicast/multicast connection, but also extends to
non-multicast connections such as multiple multicast, disjoint multicast, and
two-level multicast. We also provide sufficiency conditions for achievability
in ADT networks for any general connection set. In addition, we show that the
random linear network coding, a randomized distributed algorithm for network
code construction, achieves capacity for the connections listed above.
Finally, we extend the ADT networks to those with random erasures and cycles
(thus, allowing bi-directional links). Note that ADT network was proposed for
approximating the wireless networks; however, ADT network is acyclic.
Furthermore, ADT network does not model the stochastic nature of the wireless
links. With our algebraic framework, we incorporate both cycles as well as
random failures into ADT network model.Comment: 9 pages, 12 figures, submitted to Allerton Conferenc
Localized Dimension Growth in Random Network Coding: A Convolutional Approach
We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC)
algorithm to address the issue of field size in random network coding. ARCNC
operates as a convolutional code, with the coefficients of local encoding
kernels chosen randomly over a small finite field. The lengths of local
encoding kernels increase with time until the global encoding kernel matrices
at related sink nodes all have full rank. Instead of estimating the necessary
field size a priori, ARCNC operates in a small finite field. It adapts to
unknown network topologies without prior knowledge, by locally incrementing the
dimensionality of the convolutional code. Because convolutional codes of
different constraint lengths can coexist in different portions of the network,
reductions in decoding delay and memory overheads can be achieved with ARCNC.
We show through analysis that this method performs no worse than random linear
network codes in general networks, and can provide significant gains in terms
of average decoding delay in combination networks.Comment: 7 pages, 1 figure, submitted to IEEE ISIT 201
Network Coding for Multi-Resolution Multicast
Multi-resolution codes enable multicast at different rates to different
receivers, a setup that is often desirable for graphics or video streaming. We
propose a simple, distributed, two-stage message passing algorithm to generate
network codes for single-source multicast of multi-resolution codes. The goal
of this "pushback algorithm" is to maximize the total rate achieved by all
receivers, while guaranteeing decodability of the base layer at each receiver.
By conducting pushback and code generation stages, this algorithm takes
advantage of inter-layer as well as intra-layer coding. Numerical simulations
show that in terms of total rate achieved, the pushback algorithm outperforms
routing and intra-layer coding schemes, even with codeword sizes as small as 10
bits. In addition, the performance gap widens as the number of receivers and
the number of nodes in the network increases. We also observe that naiive
inter-layer coding schemes may perform worse than intra-layer schemes under
certain network conditions.Comment: 9 pages, 16 figures, submitted to IEEE INFOCOM 201
Decodable network coding in wireless network
Network coding is a network layer technique to improve transmission efficiency. Coding packets is especially beneficial in a wireless environment where the demand for radio spectrum is high. However, to fully realize the benefits of network coding two challenging issues that must be addressed are: (1) Guaranteeing separation of coded packets at the destination, and (2) Mitigating the extra coding/decoding delay. If the destination has all the needed packets to decode a coded packet, then separation failure can be averted. If the scheduling algorithm considers the arrival time of coding pairs, then the extra delay can be mitigated. In this paper, we develop a network coding method to address these (decoding and latency) issues for multi-source multi-destination unicast and multicast sessions. We use linear programming to find the most efficient coding design solution with guaranteed decodability. To reduce network delay, we develop a scheduling algorithm to minimize the extra coding/decoding delay. Our coding design method and scheduling algorithm are validated through experiments. Simulation results show improved transmission efficiency and reduced network delay --Abstract, page iii
Decoding communities in networks
According to a recent information-theoretical proposal, the problem of
defining and identifying communities in networks can be interpreted as a
classical communication task over a noisy channel: memberships of nodes are
information bits erased by the channel, edges and non-edges in the network are
parity bits introduced by the encoder but degraded through the channel, and a
community identification algorithm is a decoder. The interpretation is
perfectly equivalent to the one at the basis of well-known statistical
inference algorithms for community detection. The only difference in the
interpretation is that a noisy channel replaces a stochastic network model.
However, the different perspective gives the opportunity to take advantage of
the rich set of tools of coding theory to generate novel insights on the
problem of community detection. In this paper, we illustrate two main
applications of standard coding-theoretical methods to community detection.
First, we leverage a state-of-the-art decoding technique to generate a family
of quasi-optimal community detection algorithms. Second and more important, we
show that the Shannon's noisy-channel coding theorem can be invoked to
establish a lower bound, here named as decodability bound, for the maximum
amount of noise tolerable by an ideal decoder to achieve perfect detection of
communities. When computed for well-established synthetic benchmarks, the
decodability bound explains accurately the performance achieved by the best
community detection algorithms existing on the market, telling us that only
little room for their improvement is still potentially left.Comment: 9 pages, 5 figures + Appendi
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