958 research outputs found
On Coding for Reliable Communication over Packet Networks
We present a capacity-achieving coding scheme for unicast or multicast over
lossy packet networks. In the scheme, intermediate nodes perform additional
coding yet do not decode nor even wait for a block of packets before sending
out coded packets. Rather, whenever they have a transmission opportunity, they
send out coded packets formed from random linear combinations of previously
received packets. All coding and decoding operations have polynomial
complexity.
We show that the scheme is capacity-achieving as long as packets received on
a link arrive according to a process that has an average rate. Thus, packet
losses on a link may exhibit correlation in time or with losses on other links.
In the special case of Poisson traffic with i.i.d. losses, we give error
exponents that quantify the rate of decay of the probability of error with
coding delay. Our analysis of the scheme shows that it is not only
capacity-achieving, but that the propagation of packets carrying "innovative"
information follows the propagation of jobs through a queueing network, and
therefore fluid flow models yield good approximations. We consider networks
with both lossy point-to-point and broadcast links, allowing us to model both
wireline and wireless packet networks.Comment: 33 pages, 6 figures; revised appendi
Minimum-cost multicast over coded packet networks
We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved
Centralized and Cooperative Transmission of Secure Multiple Unicasts using Network Coding
We introduce a method for securely delivering a set of messages to a group of
clients over a broadcast erasure channel where each client is interested in a
distinct message. Each client is able to obtain its own message but not the
others'. In the proposed method the messages are combined together using a
special variant of random linear network coding. Each client is provided with a
private set of decoding coefficients to decode its own message. Our method
provides security for the transmission sessions against computational
brute-force attacks and also weakly security in information theoretic sense. As
the broadcast channel is assumed to be erroneous, the missing coded packets
should be recovered in some way. We consider two different scenarios. In the
first scenario the missing packets are retransmitted by the base station
(centralized). In the second scenario the clients cooperate with each other by
exchanging packets (decentralized). In both scenarios, network coding
techniques are exploited to increase the total throughput. For the case of
centralized retransmissions we provide an analytical approximation for the
throughput performance of instantly decodable network coded (IDNC)
retransmissions as well as numerical experiments. For the decentralized
scenario, we propose a new IDNC based retransmission method where its
performance is evaluated via simulations and analytical approximation.
Application of this method is not limited to our special problem and can be
generalized to a new class of problems introduced in this paper as the
cooperative index coding problem
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