15 research outputs found
Quantum processes
A number of ideas and questions related to the construction of quantum
processes are discussed. Quantum state extension, entanglement and asymptotic
behaviour of the entropy are some of the issues explored. These topics are
studied in more detail for a class of quantum processes known as finitely
correlated states. Several examples of such processes are presented,
specifically a Free Fermionic model.Comment: 20 pages, 2 figures, to appear in the proceedings of the 46th Karpacz
Winter School of Theoretical Physics "Quantum Dynamics and Information:
Theory and Experiment
On the Sensitivity of Noncoherent Capacity to the Channel Model
The noncoherent capacity of stationary discrete-time fading channels is known
to be very sensitive to the fine details of the channel model. More
specifically, the measure of the set of harmonics where the power spectral
density of the fading process is nonzero determines if capacity grows
logarithmically in SNR or slower than logarithmically. An engineering-relevant
problem is to characterize the SNR value at which this sensitivity starts to
matter.
In this paper, we consider the general class of continuous-time
Rayleigh-fading channels that satisfy the wide-sense stationary
uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread.
For this class of channels, we show that the noncoherent capacity is close to
the AWGN capacity for all SNR values of practical interest, independently of
whether the scattering function is compactly supported or not. As a byproduct
of our analysis, we obtain an information-theoretic pulse-design criterion for
orthogonal frequency-division multiplexing systems.Comment: To be presented at IEEE Int. Symp. Inf. Theory 2009, Seoul, Kore
A polynomial fit preconditioner for band Toeplitz matrices in image reconstruction
The Preconditioned Conjugate Gradient is often applied in image reconstruction as a regularizing method. When the blurring matrix has Toeplitz structure, the modified circulant preconditioner and the inverse Toeplitz preconditioner have been shown to be effective. We introduce here a preconditioner for symmetric positive definite Toeplitz matrices based on a trigonometric polynomial fit which has the same effectiveness of the previous ones but has a lower cost when applied to band matrices. The case of band block Toeplitz matrices with band Toeplitz blocks (BTTB) corresponding to separable point spread functions is also considered
Regularizing preconditioners based on fit techniques in the image reconstruction problem
Regularizing preconditioners for the approximate solution by gradient-type methods of image restoration problems with two-level band Toeplitz structure, are examined. For problems having separable and positive definite matrices, the fit preconditioner, introduced in [6], has been shown to be effective in conjunction with CG. The cost of this preconditioner is of O(n^2) operations per iteration, where n^2 is the pixels number of the image, whereas the cost of the circulant preconditioners commonly used for this type of problems is of O(n^2 log n) operations per iteration. In this paper the extension of the fit preconditioner to more general cases is proposed: namely the nonseparable positive definite case and the symmetric indefinite case are treated. The major difficulty encountered in this extension concerns the factorization phase, where, unlike the separable case, a further approximation is required. Various approximate factorizations are proposed. The preconditioners thus obtained have still a cost of O(n^2) operations per iteration. A large numerical experimentation compares these preconditioners with the circulant Chan preconditioner, showing often better performances at a lower cost
On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity
The noncoherent capacity of stationary discrete-time fading channels is known
to be very sensitive to the fine details of the channel model. More
specifically, the measure of the support of the fading-process power spectral
density (PSD) determines if noncoherent capacity grows logarithmically in SNR
or slower than logarithmically. Such a result is unsatisfactory from an
engineering point of view, as the support of the PSD cannot be determined
through measurements. The aim of this paper is to assess whether, for general
continuous-time Rayleigh-fading channels, this sensitivity has a noticeable
impact on capacity at SNR values of practical interest.
To this end, we consider the general class of band-limited continuous-time
Rayleigh-fading channels that satisfy the wide-sense stationary
uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread.
We show that, for all SNR values of practical interest, the noncoherent
capacity of every channel in this class is close to the capacity of an AWGN
channel with the same SNR and bandwidth, independently of the measure of the
support of the scattering function (the two-dimensional channel PSD). Our
result is based on a lower bound on noncoherent capacity, which is built on a
discretization of the channel input-output relation induced by projecting onto
Weyl-Heisenberg (WH) sets. This approach is interesting in its own right as it
yields a mathematically tractable way of dealing with the mutual information
between certain continuous-time random signals.Comment: final versio