Showing papers on "Biorthogonal system published in 1971"

Performance of Sequential Decoding with Biorthogonal Modulation and Q-Level Quantization

Abstract: R comp versus E_{b} / N_{0} is calculated for a coherent white Gaussian noise channel and biorthogonal signal sets with quantized and continuous correlator outputs. The results are compared with list of L detection and it is observed that the quantized scheme is more efficient. Curves of E_{b} / N_{0} for code rate R = R_{comp} versus 1/R are presented so that the efficiency of convolutional encoding and sequential decoding with various other modems can be compared for fixed rate codes.

Fundamental Biorthogonal Sequences and K-Norms on ϕ

Abstract: A biorthogonal sequence is a double sequence (xi,fi ) where each xi is from some locally convex space X, each fi is from X* and fi (xj ) = δ ij . A biorthogonal sequence is called total if the functionals (fi ) are total over X and is called fundamental if sp(xi ) is dense in X. If a biorthogonal sequence is both total and fundamental we refer to it as a Markushivich basis or, more simply, an M-basis. If (xi,fi ) is a total biorthogonal sequence for X, then X can be identified with the space of all scalar sequences (fi (x)) under the correspondence x ↔ (fi (x)). We refer to this space as the associated sequence space with respect to (xi, fi ). With this correspondence, xi corresponds to and fi corresponds to Ei , the ith coordinate functional.