Originality: This work investigated the performances of neural population coding under different correlation structures, and for the first time, it systematically clarified the conditions under which a population decoding strategy is efficient. Rigor: This work applied a combination of methods, including Information Theory, Statistical Inference and the Theory of Dynamical Systems, to analyze the performance of neural population decoding. It found that when the neuronal correlation is strong, population decoding is not as efficient as many people thought before. Significance: This work developed a new mathematical method to analyze the efficiency of neural population decoding. The results on the efficiency of population decoding have important guidance on data analysis in neurophysiology experiments. Impact: This work has important impact on our understanding of population coding, an important feature of neural information processing. It has citations: Web of Knowledge=11, Google Scholar=18.