23 research outputs found
On Coding for Cooperative Data Exchange
We consider the problem of data exchange by a group of closely-located
wireless nodes. In this problem each node holds a set of packets and needs to
obtain all the packets held by other nodes. Each of the nodes can broadcast the
packets in its possession (or a combination thereof) via a noiseless broadcast
channel of capacity one packet per channel use. The goal is to minimize the
total number of transmissions needed to satisfy the demands of all the nodes,
assuming that they can cooperate with each other and are fully aware of the
packet sets available to other nodes. This problem arises in several practical
settings, such as peer-to-peer systems and wireless data broadcast. In this
paper, we establish upper and lower bounds on the optimal number of
transmissions and present an efficient algorithm with provable performance
guarantees. The effectiveness of our algorithms is established through
numerical simulations.Comment: Appeared in the proceedings of the 2010 IEEE Information Theory
Workshop (ITW 2010, Cairo
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
Distributed Reed-Solomon Codes for Simple Multiple Access Networks
We consider a simple multiple access network in which a destination node
receives information from multiple sources via a set of relay nodes. Each relay
node has access to a subset of the sources, and is connected to the destination
by a unit capacity link. We also assume that of the relay nodes are
adversarial. We propose a computationally efficient distributed coding scheme
and show that it achieves the full capacity region for up to three sources.
Specifically, the relay nodes encode in a distributed fashion such that the
overall codewords received at the destination are codewords from a single
Reed-Solomon code.Comment: 12 pages, 1 figur
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
Coded Cooperative Data Exchange for a Secret Key
We consider a coded cooperative data exchange problem with the goal of
generating a secret key. Specifically, we investigate the number of public
transmissions required for a set of clients to agree on a secret key with
probability one, subject to the constraint that it remains private from an
eavesdropper.
Although the problems are closely related, we prove that secret key
generation with fewest number of linear transmissions is NP-hard, while it is
known that the analogous problem in traditional cooperative data exchange can
be solved in polynomial time. In doing this, we completely characterize the
best possible performance of linear coding schemes, and also prove that linear
codes can be strictly suboptimal. Finally, we extend the single-key results to
characterize the minimum number of public transmissions required to generate a
desired integer number of statistically independent secret keys.Comment: Full version of a paper that appeared at ISIT 2014. 19 pages, 2
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