16 research outputs found
Error Correction for Cooperative Data Exchange
This paper considers the problem of error correction for a cooperative data
exchange (CDE) system, where some clients are compromised or failed and send
false messages. Assuming each client possesses a subset of the total messages,
we analyze the error correction capability when every client is allowed to
broadcast only one linearly-coded message. Our error correction capability
bound determines the maximum number of clients that can be compromised or
failed without jeopardizing the final decoding solution at each client. We show
that deterministic, feasible linear codes exist that can achieve the derived
bound. We also evaluate random linear codes, where the coding coefficients are
drawn randomly, and then develop the probability for a client to withstand a
certain number of compromised or failed peers and successfully deduce the
complete message for any network size and any initial message distributions
Estimating Minimum Sum-rate for Cooperative Data Exchange
This paper considers how to accurately estimate the minimum sum-rate so as to
reduce the complexity of solving cooperative data exchange (CDE) problems. The
CDE system contains a number of geographically close clients who send packets
to help the others recover an entire packet set. The minimum sum-rate is the
minimum value of total number of transmissions that achieves universal recovery
(the situation when all the clients recover the whole packet set). Based on a
necessary and sufficient condition for a supermodular base polyhedron to be
nonempty, we show that the minimum sum-rate for a CDE system can be determined
by a maximization over all possible partitions of the client set. Due to the
high complexity of solving this maximization problem, we propose a
deterministic algorithm to approximate a lower bound on the minimum sum-rate.
We show by experiments that this lower bound is much tighter than those lower
bounds derived in the existing literature. We also show that the deterministic
algorithm prevents from repetitively running the existing algorithms for
solving CDE problems so that the overall complexity can be reduced accordingly.Comment: 6 pages, 6 figure
Cooperative Data Exchange with Unreliable Clients
Consider a set of clients in a broadcast network, each of which holds a
subset of packets in the ground set X. In the (coded) cooperative data exchange
problem, the clients need to recover all packets in X by exchanging coded
packets over a lossless broadcast channel. Several previous works analyzed this
problem under the assumption that each client initially holds a random subset
of packets in X. In this paper we consider a generalization of this problem for
settings in which an unknown (but of a certain size) subset of clients are
unreliable and their packet transmissions are subject to arbitrary erasures.
For the special case of one unreliable client, we derive a closed-form
expression for the minimum number of transmissions required for each reliable
client to obtain all packets held by other reliable clients (with probability
approaching 1 as the number of packets tends to infinity). Furthermore, for the
cases with more than one unreliable client, we provide an approximation
solution in which the number of transmissions per packet is within an
arbitrarily small additive factor from the value of the optimal solution.Comment: 8 pages; in Proc. 53rd Annual Allerton Conference on Communication,
Control, and Computing (Allerton 2015
Iterative Merging Algorithm for Cooperative Data Exchange
We consider the problem of finding the minimum sum-rate strategy in
cooperative data exchange systems that do not allow packet-splitting (NPS-CDE).
In an NPS-CDE system, there are a number of geographically close cooperative
clients who send packets to help the others recover a packet set. A minimum
sum-rate strategy is the strategy that achieves universal recovery (the
situation when all the clients recover the whole packet set) with the the
minimal sum-rate (the total number of transmissions). We propose an iterative
merging (IM) algorithm that recursively merges client sets based on a lower
estimate of the minimum sum-rate and updates to the value of the minimum
sum-rate. We also show that a minimum sum-rate strategy can be learned by
allocating rates for the local recovery in each merged client set in the IM
algorithm. We run an experiment to show that the complexity of the IM algorithm
is lower than that of the existing deterministic algorithm when the number of
clients is lower than .Comment: 9 pages, 3 figure
Network Codes for Real-Time Applications
We consider the scenario of broadcasting for real-time applications and loss
recovery via instantly decodable network coding. Past work focused on
minimizing the completion delay, which is not the right objective for real-time
applications that have strict deadlines. In this work, we are interested in
finding a code that is instantly decodable by the maximum number of users.
First, we prove that this problem is NP-Hard in the general case. Then we
consider the practical probabilistic scenario, where users have i.i.d. loss
probability and the number of packets is linear or polynomial in the number of
users. In this scenario, we provide a polynomial-time (in the number of users)
algorithm that finds the optimal coded packet. The proposed algorithm is
evaluated using both simulation and real network traces of a real-time Android
application. Both results show that the proposed coding scheme significantly
outperforms the state-of-the-art baselines: an optimal repetition code and a
COPE-like greedy scheme.Comment: ToN 2013 Submission Versio
Efficient Algorithms for the Data Exchange Problem
In this paper we study the data exchange problem where a set of users is
interested in gaining access to a common file, but where each has only partial
knowledge about it as side-information. Assuming that the file is broken into
packets, the side-information considered is in the form of linear combinations
of the file packets. Given that the collective information of all the users is
sufficient to allow recovery of the entire file, the goal is for each user to
gain access to the file while minimizing some communication cost. We assume
that users can communicate over a noiseless broadcast channel, and that the
communication cost is a sum of each user's cost function over the number of
bits it transmits. For instance, the communication cost could simply be the
total number of bits that needs to be transmitted. In the most general case
studied in this paper, each user can have any arbitrary convex cost function.
We provide deterministic, polynomial-time algorithms (in the number of users
and packets) which find an optimal communication scheme that minimizes the
communication cost. To further lower the complexity, we also propose a simple
randomized algorithm inspired by our deterministic algorithm which is based on
a random linear network coding scheme.Comment: submitted to Transactions on Information Theor
On the Optimality of Secret Key Agreement via Omniscience
For the multiterminal secret key agreement problem under a private source
model, it is known that the maximum key rate, i.e., the secrecy capacity, can
be achieved through communication for omniscience, but the omniscience strategy
can be strictly suboptimal in terms of minimizing the public discussion rate.
While a single-letter characterization is not known for the minimum discussion
rate needed for achieving the secrecy capacity, we derive single-letter lower
and upper bounds that yield some simple conditions for omniscience to be
discussion-rate optimal. These conditions turn out to be enough to deduce the
optimality of omniscience for a large class of sources including the
hypergraphical sources. Through conjectures and examples, we explore other
source models to which our methods do not easily extend