This paper studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean squared error. It is shown that when a symmetric source density with infinite support is sufficiently well behaved, the optimal step size ∆ N for symmetric uniform scalar quantization decreases as 2σ N −1 V −1 1 / 6N 2

Abstract-A method of constructing rate-compatible polar codes that are capacity-achieving with low-complexity sequential decoders is presented. The proposed code construction allows for incremental retransmissions at different rates in order to adapt to channel conditions. The main idea of the construction exploits certain common characteristics of polar codes that are optimized for a sequence of successively degraded channels. The proposed approach allows for an optimized polar code to be used at every transmission thereby achieving capacity. Due to the length limitation of conventional polar codes, the proposed construction can only support a restricted set of rates that is characterized by the size of the kernel when conventional polar codes are used. To overcome this limitation, punctured polar codes which provide more flexibility on block length by controlling a puncturing fraction are considered. The existence of capacity-achieving punctured polar codes for any given puncturing fraction is shown. Using punctured polar codes as constituent codes, it is shown that the proposed rate-compatible polar code is capacity-achieving for an arbitrary sequence of rates and for any class of degraded channels.

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This paper addresses distributed parameter coordination methods for wireless communication systems. This proposes a method based on a message-passing algorithm, namely min-sum algorithm, on factor graphs for the application of precoder selection. Two particular examples of precoder selection are considered: transmit antenna selection and beam selection. Evaluations on the potential of such an approach in a wireless communication network are provided, and its performance and convergence properties are compared with those of a baseline selfish/greedy approach. Simulation results for the precoder selection examples are presented and discussed, which show that the graph-based technique generally obtains gain in sum rate over the greedy approach at the cost of a larger message size. Besides, the proposed method usually reaches the global optima in an efficient manner. Methods of improving the rate of convergence of the graph-based distributed coordination technique and reducing its associated message size are therefore important topics for wireless communication networks.

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