Asymptotic Behavior of Error Exponents in the Wideband Regime

DOI10.1109/TIT.2007.892786zbMATH Open1205.94043arXivcs/0509001MaRDI QIDQ3548237

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Publication date: 21 December 2008

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Abstract: In this paper, we complement Verd'{u}'s work on spectral efficiency in the wideband regime by investigating the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent. Specifically, we consider both AWGN and Rayleigh-fading channels. For the AWGN channel model, the optimal values of $R_z(0)$ and $dot{R}_z(0)$ are calculated, where $R_z(1/B)$ is the maximum rate at which information can be transmitted over a channel with bandwidth $B/2$ when the error-exponent is constrained to be greater than or equal to $z.$ Based on this calculation, we say that a sequence of input distributions is near optimal if both $R_z(0)$ and $dot{R}_z(0)$ are achieved. We show that QPSK, a widely-used signaling scheme, is near-optimal within a large class of input distributions for the AWGN channel. Similar results are also established for a fading channel where full CSI is available at the receiver.

Full work available at URL: https://arxiv.org/abs/cs/0509001

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