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This thesis is concerned with decoding for wireless communications. In particular, computationally efficient lattice decoding algorithms are exploited to further improve the system performance. Based on this idea, five technical chapters are presented in this thesis. In Chapter 2, we propose novel lattice decoding based on segment Lenstra-Lenstra-Lovász (LLL) algorithm to further reduce the decoding complexity of coded Multiple-Input Multiple-Output (MIMO) cooperative channel. In particular, we extend the original segment LLL algorithm to the complex version, and prove that it can achieve the optimal diversity-multiplexing tradeoff (DMT). In Chapter 3, we present randomized lattice decoding based on Klein's sampling technique, which is a randomized version of Babai's nearest plane algorithm (i.e., successive interference cancellation). We analyze and optimize the performance of randomized lattice decoding resulting in reduced decoding complexity, and propose a very efficient implementation of random rounding. Chapter 4 is concerned with bounded distance decoding (BDD) based embedding technique. The embedding technique is used to reduce the γ-BDD problem to 1/(2γ)-unique shortest vector problem 1/(2γ)-uSVP). WE prove that the Lenstra, Lenstra and Lovász (LLL) algorithm can achieve 1/(2γ)-BDD for γ ≈ O(2n) for embedding decoding. We also prove that BDD of the regularized lattice is optimal in terms of the DMT. In Chapter 5, we present a detailed study of the soft output MIMO decoding. We show that the randomized decoding algorithm is an efficient way to compute soft output. In order to improve soft output quality, we propose variants of soft output decoding based on the sampling technique and embedding technique. Moreover, we derive a lower bound on the search radius for which list-based decoding can provide a near optimal solution to soft output. In Chapter 6, the performance limits of lattice reduction-aided precoding are investigated. The proximity factor is defined to measure the worst-case transmission power gap to sphere precoding. The second moment over precoding region is defined to measure the average-case transmission power loss. Afterward, low dimension lattice precoding is proposed to further reduce the transmission power. |
