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A new algorithm of matrix spectral factorization is proposed which can be applied to compute an approximate spectral factor of any positive definite matrix function which satisfies the Paley-Wiener condition. ref refid="fnote1"/ id="fnote1" asterisk="no"paraThis paper includes the detailed proofs for an innovative method for matrix spectral factorization that can be used in numerous applications, including filtering, data compression, and wireless communications. A U.S. patent application has been submitted for this innovation through the Technology Commercialization Center, University of Maryland.para [ABSTRACT FROM AUTHOR]

Given an m × n array of k single random error correction (or erasure) codewords, each having length l such that mn = kl, we construct optimal interleaving schemes that provide the maximum burst error correction power such that an arbitrarily shaped error burst of size can be corrected for the largest possible value of t. We show that for all such m × n arrays, the maximum possible interleaving distance, or equivalently, the largest value oft such that an arbitrary error burst of size up tot can be corrected, is bounded by └√2k┘ if k ≤, ┌(min{m, n})²/2┐, and by min{m, n} + └(k - ┌(min{m, n})²/2┐)/min{m, n}┘ if k ≥ ┌(min{m, n} )²/2]. We generalize the cyclic shifting algorithm developed by the authors in a previous paper and construct, in several special cases, optimal interleaving arrays achieving these upper bounds. Additionally, for codewords of variable lengths, we solve a related array coloring problem for which the same upper bounds hold and can be achieved. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of joint permutor analysis and design for J-dimensional multiple turbo codes with J constituent encoders, J > 2. The concept of summary distance is extended to multiple permutors of size N and used as the design metric. Using the sphere-packing concept, we prove that the minimum length-2 summary distance (spread) Dmin, 2 is asymptoticly upper-bounded by O(NJ-1/Jr). We also show that the asymptotic minimum length-2L summary distance Dmin, 2L for the class of random permutors is lower-bounded by O (NJ-2/J-ϵ ), where ϵ > 0 can be arbitrarily small. Then, using the technique of expurgating "bad" symbols, we show that the spread of random permutors can achieve the optimum growth rate, i.e., O (NJ-1/J ), and that the asymptotic growth rate of Dmin, 2L can also be improved. The minimum length-2 and length-4 summary distances are studied for an important practical class of permutors-linear permutors. We prove that there exist J-dimensional multiple linear permutors with optimal spread Dmin, 2 = O(NJ-1/J ). Finally, we present several joint permutor construction algorithms applicable to multiple turbo codes of short and medium lengths. [ABSTRACT FROM AUTHOR]