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

Generalized polyphase representation and application to coding gain enhancement

Generalized polyphase representations (GPP) have been mentioned in literature in the context of several applications. In this paper, we provide a characterization for what constitutes a valid GPP. Then, we study an application of GPP, namely in improving the coding gains of transform coding systems. We also prove several properties of the GPP

Coding gain in paraunitary analysis/synthesis systems

A formal proof that bit allocation results hold for the entire class of paraunitary subband coders is presented. The problem of finding an optimal paraunitary subband coder, so as to maximize the coding gain of the system, is discussed. The bit allocation problem is analyzed for the case of the paraunitary tree-structured filter banks, such as those used for generating orthonormal wavelets. The even more general case of nonuniform filter banks is also considered. In all cases it is shown that under optimal bit allocation, the variances of the errors introduced by each of the quantizers have to be equal. Expressions for coding gains for these systems are derived

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

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