5,920 research outputs found
Empirical and Strong Coordination via Soft Covering with Polar Codes
We design polar codes for empirical coordination and strong coordination in
two-node networks. Our constructions hinge on the fact that polar codes enable
explicit low-complexity schemes for soft covering. We leverage this property to
propose explicit and low-complexity coding schemes that achieve the capacity
regions of both empirical coordination and strong coordination for sequences of
actions taking value in an alphabet of prime cardinality. Our results improve
previously known polar coding schemes, which (i) were restricted to uniform
distributions and to actions obtained via binary symmetric channels for strong
coordination, (ii) required a non-negligible amount of common randomness for
empirical coordination, and (iii) assumed that the simulation of discrete
memoryless channels could be perfectly implemented. As a by-product of our
results, we obtain a polar coding scheme that achieves channel resolvability
for an arbitrary discrete memoryless channel whose input alphabet has prime
cardinality.Comment: 14 pages, two-column, 5 figures, accepted to IEEE Transactions on
Information Theor
Strong Coordination with Polar Codes
In this paper, we design explicit codes for strong coordination in two-node
networks. Specifically, we consider a two-node network in which the action
imposed by nature is binary and uniform, and the action to coordinate is
obtained via a symmetric discrete memoryless channel. By observing that polar
codes are useful for channel resolvability over binary symmetric channels, we
prove that nested polar codes achieve a subset of the strong coordination
capacity region, and therefore provide a constructive and low complexity
solution for strong coordination.Comment: 7 pages doublespaced, presented at the 50th Annual Allerton
Conference on Communication, Control and Computing 201
Information Design for Strategic Coordination of Autonomous Devices with Non-Aligned Utilities
In this paper, we investigate the coordination of autonomous devices with
non-aligned utility functions. Both encoder and decoder are considered as
players, that choose the encoding and the decoding in order to maximize their
long-run utility functions. The topology of the point-to-point network under
investigation, suggests that the decoder implements a strategy, knowing in
advance the strategy of the encoder. We characterize the encoding and decoding
functions that form an equilibrium, by using empirical coordination. The
equilibrium solution is related to an auxiliary game in which both players
choose some conditional distributions in order to maximize their expected
utilities. This problem is closely related to the literature on "Information
Design" in Game Theory. We also characterize the set of posterior distributions
that are compatible with a rate-limited channel between the encoder and the
decoder. Finally, we provide an example of non-aligned utility functions
corresponding to parallel fading multiple access channels.Comment: IEEE Proc. of the Fifty-fourth Annual Allerton Conference Allerton
House, UIUC, Illinois, USA September 27 - 30, 201
Secure Cascade Channel Synthesis
We consider the problem of generating correlated random variables in a
distributed fashion, where communication is constrained to a cascade network.
The first node in the cascade observes an i.i.d. sequence locally before
initiating communication along the cascade. All nodes share bits of common
randomness that are independent of . We consider secure synthesis - random
variables produced by the system appear to be appropriately correlated and
i.i.d. even to an eavesdropper who is cognizant of the communication
transmissions. We characterize the optimal tradeoff between the amount of
common randomness used and the required rates of communication. We find that
not only does common randomness help, its usage exceeds the communication rate
requirements. The most efficient scheme is based on a superposition codebook,
with the first node selecting messages for all downstream nodes. We also
provide a fleeting view of related problems, demonstrating how the optimal rate
region may shrink or expand.Comment: Submitted to IEEE Transactions on Information Theor
Source-channel coding for coordination over a noisy two-node network
Recently, the concept of coordinating actions between distributed agents has emerged in the information theory literature. It was first introduced by Cuff in 2008 for the point-to-point case of coordination. However, Cuffâs work and the vast majority of the follow-up research are based on establishing coordination over noise-free communication links. In contrast, this thesis investigates the open problem of coordination over noisy point-to-point links. The aim of this study is to examine Shannonâs source-channel separation theorem in the context of coordination. To that end, a general joint scheme to achieve the strong notion of coordination over a discrete memoryless channel is introduced. The strong coordination notion requires that the L1 distance between the induced joint distribution of action sequences selected by the nodes and a prescribed joint distribution vanishes exponentially fast with the sequence block length. From the general joint scheme, three special cases are constructed, one of which resembles Shannonâs separation scheme. As a surprising result, the proposed joint scheme has been found to be able to perform better than a strictly separate scheme. Finally, the last part of the thesis provides simulation results to confirm the presented argument based on comparing the achievable rate regions for the scheme resembling Shannonâs separation and a special case of the general joint scheme
Smoothing of binary codes, uniform distributions, and applications
The action of a noise operator on a code transforms it into a distribution on
the respective space. Some common examples from information theory include
Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting
on a lattice in the Euclidean space. We aim to characterize the cases when the
output distribution is close to the uniform distribution on the space, as
measured by R{\'e}nyi divergence of order . A version of
this question is known as the channel resolvability problem in information
theory, and it has implications for security guarantees in wiretap channels,
error correction, discrepancy, worst-to-average case complexity reductions, and
many other problems.
Our work quantifies the requirements for asymptotic uniformity (perfect
smoothing) and identifies explicit code families that achieve it under the
action of the Bernoulli and ball noise operators on the code. We derive
expressions for the minimum rate of codes required to attain asymptotically
perfect smoothing. In proving our results, we leverage recent results from
harmonic analysis of functions on the Hamming space. Another result pertains to
the use of code families in Wyner's transmission scheme on the binary wiretap
channel. We identify explicit families that guarantee strong secrecy when
applied in this scheme, showing that nested Reed-Muller codes can transmit
messages reliably and securely over a binary symmetric wiretap channel with a
positive rate. Finally, we establish a connection between smoothing and error
correction in the binary symmetric channel
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