This work investigates high-SNR outage behavior of slow fading channels with quantized feedback and partial power control, when feedback indices are error-prone. We propose a quantizer structure with continuous Voronoi regions and derive its optimality conditions using probability analysis. Our design involves construction of a novel bit-mapping scheme. The optimized power control codebook resembles channel optimized scalar quantizers (COSQs). Also, the diversity gain of the communication system under study is characterized with both nonzero and vanishing feedback error probabilities.
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Ekbatani et al. (2010) studied this question.
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