submit
english version rss feed

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research papers, whether they are published or not, and for PhD dissertation. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

New submissions 
Chemical Sciences
Cognitive science
Computer Science
Engineering Sciences
Environmental Sciences
Humanities and Social Sciences
Life Sciences
Mathematics
Nonlinear Sciences
Physics
Quantitative Finance
Sciences of the Universe
Statistics
It is now well known that curvature conditions à la Bakry-Emery are equivalent to contraction properties of the heat semigroup with respect to the classical quadratic Wasserstein distance. However, this curvature condition may include a dimensional correction which up to now had not induced any strenghtening of this contraction. We first consider the simplest example of the Euclidean heat semigroup, and prove that indeed it is so. To consider the case of a general Markov semigroup, we introduce a new distance between probability measures, based on the semigroup, and adapted to it. We prove that this Markov transportation distance satisfies the same properties for a general Markov semigroup as the Wasserstein distance does in the specific case of the Euclidean heat semigroup, namely dimensional contraction properties and Evolutional variational inequalities.
This paper considers a Gaussian relay network where a source transmits a message to a destination with the help of N half-duplex relays. The information theoretic cut-set upper bound to the capacity is shown to be achieved to within 1.96(N+2) bits by noisy network coding, thereby reducing the previously known gap. This gap is obtained as a special case of a more general constant gap result for Gaussian half-duplex multicast networks. It is then shown that the generalized Degrees-of-Freedom of this network is the solution of a linear program, where the coefficients of the linear inequality constraints are proved to be the solution of several linear programs referred as the assignment problem in graph theory, for which efficient numerical algorithms exist. The optimal schedule, that is, the optimal value of the 2N possible transmit-receive configuration states for the relays, is investigated and known results for diamond networks are extended to general relay networks. It is shown, for the case of N=2 relays, that only N+1=3 out of the 2^N=4 possible states have a strictly positive probability and suffice to characterize the capacity to within a constant gap. Extensive experimental results show that, for a general N-relay network with N<8, the optimal schedule has at most N+1 states with a strictly positive probability. As an extension of a conjecture presented for diamond networks, it is conjectured that this result holds for any HD relay network and any number of relays. Finally, a network with N=2 relays is studied in detail to illustrate the channel conditions under which selecting the best relay is not optimal, and to highlight the nature of the rate gain due to multiple relays.
This paper considers the Gaussian half-duplex relay channel (G-HD-RC): a channel model where a source transmits a message to a destination with the help of a relay that can not transmit and receive at the same time. It is shown that the cut-set upper bound on the capacity can be achieved to within a constant gap, regardless of the actual value of the channel parameters, by either Partial-Decode-and-Forward or Compress-and-Forward. The performance of these coding strategies is evaluated with both random and deterministic switch at the relay. Numerical evaluations show that the actual gap is less than what analytically obtained, and that random switch achieves higher rates than deterministic switch. As a result of this analysis, the generalized Degrees-of-Freedom of the G-HD-RC is exactly characterized for this channel. In order to get insights into practical schemes for the G-HD-RC that are less complex than Partial-Decode-and-Forward or Compress-and-Forward, the exact capacity of the Linear Deterministic Approximation (LDA) of the G-HD-RC at high-SNR is determined. It is shown that random switch and correlated non-uniform inputs bits are optimal for the LDA. It is then demonstrated that deterministic switch is to within one bit from the capacity. This latter scheme is translated into a coding strategy for the original G-HD-RC and its optimality to within a constant gap is proved. The gap attained by this scheme is larger than that of Partial-Decode-and-Forward, thereby pointing to an interesting practical tradeoff between gap to capacity and complexity.
For contributors 
  • The deposit of a document requires the agreement of all its authors, and it must respect editor policy
  • A submitted document passed a moderation process. It can be rejected if it does not fullfill HAL criteria (see contributor guide)
  • Once a document is put online, it cannot be withdrawn
  • Refer to the manuHAL
For readers 
  • Within the context of electronic communication, rules about intellectual property do apply. In particular, authors must be correctly recognized as such, and their work must be cited if used.
Terms of Use
  • HAL metadata may be totally or in part browsed by OAI-PMH harvesting ;
  • No commercial use of the extracted data ;
  • The source must be cited (eg hal.archives-ouvertes.fr/hal-00000001).

  Submit
Login
Password
registerforgot your password?
  Documents with fulltext
282435
  Submission evolution
  Contact
 - support.ccsd.cnrs.fr
 - 
  News
HAL v3 : come and try ! (2014-03-31)
HAL v3 : author, idHAL and CV (2014-03-26)
Accounts and profiles: what changes in HAL v3 (2014-03-21)
Digital identities and open archives (2013-12-13)
  Video

all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...