11,405 research outputs found
A complete factorization of paraunitary matrices with pairwise mirror-image symmetry in the frequency domain
The problem of designing orthonormal (paraunitary) filter banks has been addressed in the past. Several structures have been reported for implementing such systems. One of the structures reported imposes a pairwise mirror-image symmetry constraint on the frequency responses of the analysis (and synthesis) filters around π/2. This structure requires fewer multipliers, and the design time is correspondingly less than most other structures. The filters designed also have much better attenuation.
In this correspondence, we characterize the polyphase matrix of the above filters in terms of a matrix equation. We then prove that the structure reported in a paper by Nguyen and Vaidyanathan, with minor modifications, is complete. This means that every polyphase matrix whose filters satisfy the mirror-image property can be factorized in terms of the proposed structure
A digital interface for Gaussian relay networks: lifting codes from the discrete superposition model to Gaussian relay networks
For every Gaussian relay network with a single source-destination pair, it is
known that there exists a corresponding deterministic network called the
discrete superposition network that approximates its capacity uniformly over
all SNR's to within a bounded number of bits. The next step in this program of
rigorous approximation is to determine whether coding schemes for discrete
superposition models can be lifted to Gaussian relay networks with a bounded
rate loss independent of SNR. We establish precisely this property and show
that the superposition model can thus serve as a strong surrogate for designing
codes for Gaussian relay networks.
We show that a code for a Gaussian relay network, with a single
source-destination pair and multiple relay nodes, can be designed from any code
for the corresponding discrete superposition network simply by pruning it. In
comparison to the rate of the discrete superposition network's code, the rate
of the Gaussian network's code only reduces at most by a constant that is a
function only of the number of nodes in the network and independent of channel
gains.
This result is also applicable for coding schemes for MIMO Gaussian relay
networks, with the reduction depending additionally on the number of antennas.
Hence, the discrete superposition model can serve as a digital interface for
operating Gaussian relay networks.Comment: 5 pages, 2010 IEEE Information Theory Workshop, Cair
A digital interface for Gaussian relay and interference networks: Lifting codes from the discrete superposition model
For every Gaussian network, there exists a corresponding deterministic
network called the discrete superposition network. We show that this discrete
superposition network provides a near-optimal digital interface for operating a
class consisting of many Gaussian networks in the sense that any code for the
discrete superposition network can be naturally lifted to a corresponding code
for the Gaussian network, while achieving a rate that is no more than a
constant number of bits lesser than the rate it achieves for the discrete
superposition network. This constant depends only on the number of nodes in the
network and not on the channel gains or SNR. Moreover the capacities of the two
networks are within a constant of each other, again independent of channel
gains and SNR. We show that the class of Gaussian networks for which this
interface property holds includes relay networks with a single
source-destination pair, interference networks, multicast networks, and the
counterparts of these networks with multiple transmit and receive antennas.
The code for the Gaussian relay network can be obtained from any code for the
discrete superposition network simply by pruning it. This lifting scheme
establishes that the superposition model can indeed potentially serve as a
strong surrogate for designing codes for Gaussian relay networks.
We present similar results for the K x K Gaussian interference network, MIMO
Gaussian interference networks, MIMO Gaussian relay networks, and multicast
networks, with the constant gap depending additionally on the number of
antennas in case of MIMO networks.Comment: Final versio
Corrections and acknowledgment for ``Local limit theory and large deviations for supercritical branching processes''
Corrections and acknowledgment for ``Local limit theory and large deviations
for supercritical branching processes'' [math.PR/0407059]Comment: Published at http://dx.doi.org/10.1214/105051606000000574 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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