In Sook Park | Searcharxiv

arXiv2009

Efficient decoding algorithm using triangularity of $\mbf{R}$ matrix of QR-decomposition

An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides various combinations of two or more different searching algorithms. Hence it makes flexibility in error rate and complexity for the algorithms using it. We calculate diversity orders and upper bounds of error rates for typical models when these models are solved by divided decodings with sphere decoder, and discuss about the effects of divided decoding on complexity. Simulation results of divided decodings combined with a sphere decoder according to different splitting indices correspond to the theoretical analysis.

cs.IT↗

arXiv2003

On the Vector valued Fourier Transform And Compatibility of Operators

Let $\mathbb{G}$ be a locally compact abelian group and let $1<p\leq 2$. $\mathbb{G}^{'}$ is the dual group of $\mathbb{G}$, and $p^{'}$ the conjugate exponent of $p$. An operator $T$ between Banach spaces $X$ and $Y$ is said to be compatible with the Fourier transform $F^{\mathbb{G}}$ if $F^{\mathbb{G}}\otimes T: L_p(\mathbb{G})\otimes X\to L_{p^{'}}(\mathbb{G}^{'})\otimes Y $ admits a continuous extension $[F^{\mathbb{G}},T]:[L_p(\mathbb{G}),X]\to [L_{p^{'}}(\mathbb{G}^{'}),Y]$. $\mathcal{FT}_p^{\mathbb{G}}$ denotes the set of such $T$'s. We show that $\mathcal{FT}_p^{\mathbb{R}\times\mathbb{G}}=\mathcal{FT}_p^{\mathbb{Z}\times\m athbb{G}} =\mathcal{FT}_p^{\mathbb{Z}^n \times\mathbb{G}}$ for any $\mathbb{G}$ and positive integer $n$. And if the factor group of $\mathbb{G}$ with respect to its component of the identity element is a direct sum of a torsion free group and a finite group with discrete topology then $\mathcal{FT}_p^{\mathbb{G}}=\mathcal{FT}_p^{\mathbb{Z}}$ .

math.FA↗