3,666 research outputs found
Multicast Network Coding and Field Sizes
In an acyclic multicast network, it is well known that a linear network
coding solution over GF() exists when is sufficiently large. In
particular, for each prime power no smaller than the number of receivers, a
linear solution over GF() can be efficiently constructed. In this work, we
reveal that a linear solution over a given finite field does \emph{not}
necessarily imply the existence of a linear solution over all larger finite
fields. Specifically, we prove by construction that: (i) For every source
dimension no smaller than 3, there is a multicast network linearly solvable
over GF(7) but not over GF(8), and another multicast network linearly solvable
over GF(16) but not over GF(17); (ii) There is a multicast network linearly
solvable over GF(5) but not over such GF() that is a Mersenne prime
plus 1, which can be extremely large; (iii) A multicast network linearly
solvable over GF() and over GF() is \emph{not} necessarily
linearly solvable over GF(); (iv) There exists a class of
multicast networks with a set of receivers such that the minimum field size
for a linear solution over GF() is lower bounded by
, but not every larger field than GF() suffices to
yield a linear solution. The insight brought from this work is that not only
the field size, but also the order of subgroups in the multiplicative group of
a finite field affects the linear solvability of a multicast network
Evaluation of Multicasting Schemes based on Joint Multiple Description and Network Coding
International audienceThis paper considers a multicast scenario and compares the average reception quality obtained when combining multiple description coding (MDC) and network coding (NC). Plain (single description) network coding (NC-SDC) serves as reference. In the considered scenario, a single source is multicast to several receivers with various channel conditions. Contrary to a NC-SDC scheme, unable to recover the coded packets when not enough combinations of packets have been received, NC of MDC packets allows a more progressive quality improvement with the number of received packets, and a reduction of the effect of the quantization noise when MDC is performed via frame expansion before quantization. Considering a probability distribution for the bit transition probability during transmission to any user in the multicast group, the expected signal-to-noise ratio is evaluated. Performance comparisons are made for various error distributions, field sizes, and MDC methods (via frame expansion and correlating transform)
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
On the utility of network coding in dynamic environments
Many wireless applications, such as ad-hoc networks and sensor networks, require decentralized operation in dynamically varying environments. We consider a distributed randomized network coding approach that enables efficient decentralized operation of multi-source multicast networks. We show that this approach provides substantial benefits over traditional routing methods in dynamically varying environments. We present a set of empirical trials measuring the performance of network coding versus an approximate online Steiner tree routing approach when connections vary dynamically. The results show that network coding achieves superior performance in a significant fraction of our randomly generated network examples. Such dynamic settings represent a substantially broader class of networking problems than previously recognized for which network coding shows promise of significant practical benefits compared to routing
Network monitoring in multicast networks using network coding
In this paper we show how information contained in robust network codes can be used for passive inference of possible locations of link failures or losses in a network. For distributed randomized network coding, we bound the probability of being able to distinguish among a given set of failure events, and give some experimental results for one and two link failures in randomly generated networks. We also bound the required field size and complexity for designing a robust network code that distinguishes among a given set of failure events
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