In this thesis, we propose an algorithm to reduce the complexity to search the most suitable codeword for a given codebook. It is proven in the thesis that about half codewords are eliminated in each iteration. In addition, we derive two lower bounds for the proposed algorithm and show that they reach the actual SNR loss in high resolution codebook. Furthermore, the complexity analysis and simulations are given to see that the advantages of taking this algorithm are revealed in the scenario of large codebook size.