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A Geometric Analysis of the AWGN Channel With a $(\sigma , \rho )$ -Power Constraint.
- Source :
-
IEEE Transactions on Information Theory . Aug2016, Vol. 62 Issue 8, p4413-4438. 26p. - Publication Year :
- 2016
-
Abstract
- In this paper, we consider the additive white Gaussian noise (AWGN) channel with a power constraint called the (\sigma , \rho ) -power constraint, which is motivated by energy harvesting communication systems. Given a codeword, the constraint imposes a limit of \sigma + k \rho on the total power of any k\geq 1 consecutive transmitted symbols. Such a channel has infinite memory and evaluating its exact capacity is a difficult task. Consequently, we establish an n , which is the set of all length n sequences satisfying the (\sigma , \rho ) -power constraints. For a noise power of \nu , which is the Minkowski sum of {\mathcal{ S}}_{n}(\sigma , \rho ) and the n -dimensional Euclidean ball of radius \sqrt n\nu . We analyze this bound using a result from convex geometry known as Steiner’s formula, which gives the volume of this Minkowski sum in terms of the intrinsic volumes of \mathcal Sn(\sigma , \rho ) . We show that as the dimension n increases, the logarithm of the sequence of intrinsic volumes of \{ {\mathcal{ S}}_{n}(\sigma , \rho )\} converges to a limit function under an appropriate scaling. The upper bound on capacity is then expressed in terms of this limit function. We derive the asymptotic capacity in the low- and high-noise regime for the (\sigma , \rho )$ -power constrained AWGN channel, with strengthened results for the special case of $\sigma = 0$ , which is the amplitude constrained AWGN channel. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 62
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 116814324
- Full Text :
- https://doi.org/10.1109/TIT.2016.2580545