Abstract-This study presents novel methods for computing fixed points of positive concave mappings and for characterizing the existence of fixed points. These methods are particularly important in planning and optimization tasks in wireless networks. For example, previous studies have shown that the feasibility of a network design can be quickly evaluated by computing the fixed point of a concave mapping that is constructed based on many environmental and network control parameters such as the position of base stations, channel conditions, and antenna tilts. To address this and more general problems, given a positive concave mapping, we show two alternative but equivalent ways to construct a matrix that is guaranteed to have spectral radius strictly smaller than one if the mapping has a fixed point. This matrix is then used to build a new mapping that preserves the fixed point of the original positive concave mapping. We show that the standard fixed point iterations using the new mapping converges faster than the standard iterations applied to the original concave mapping. As exemplary applications of the proposed methods, we consider the problems of power and load estimation in networks based on the orthogonal frequency division multiple access (OFDMA) technology.

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With rapid increase of image resolution in modern video processing and display systems, the bandwidth and power consumption of external memory are becoming serious bottlenecks. This problem can be alleviated by highfidelity embedded compression (EC) techniques for video frame buffers. Classic lossless or near-lossless coding methods like CALIC are ill suited for embedded systems due to their high complexity. In this work, a new, simple infra-frame EC technique based on downsampling and side-information aided upsampling is developed. Through a study of a family of downsampling schemes, an optimal one is found and analyzed for EC. This downsampling scheme gives birth to the new EC technique. The main idea is to first split an image into blocks, and then adaptively choose different down sampling patterns and upsampling methods to code/decode these blocks. For a memory bandwidth reduction of 60%, the proposed EC system can achieve PSNR above 40dB, while allowing very simple, low-cost real-time hardware realization. A noteworthy novelty of this work is compression without entropy coding. The resulting code stream is of fixed-rate, supporting random access to pixel blocks. Keywords-embedded compression, downsampling pattern, adaptive coding I.978-1-4799-8391-9/15/$31.00 ©2015 IEEE