Vector Quantization: Theoretical Limits and Practical Constructions

研究人员对矢量量化中与维度和速率之间的权衡相关的问题进行了系统的研究。他们研究了通过同时量化数据块而不是标量量化可以获得的压缩增益。对于最坏情况和平均情况的性能标准，寻求关于节省、收敛速度和实现它们的算法的理论极限。特别考虑的是只达到两个值的“组合”失真度量：零或无穷大。这些措施只允许某些类型的错误，并且在某些错误不可容忍的应用程序中很重要。这些指标更易于分析，但也显示了一般指标的许多复杂性。

The investigators perform a systematic study of issues related to the tradeoffs between dimension and rate in vector quantization. They investigate the compression gains achievable by simultaneous quantization of a block of data over scalar quantization. Theoretical limits on the savings, rates of convergence, and algorithms achieving them are sought for worst-case as well as average-case performance criteria. Special consideration is given to "combinatorial" distortion measures that attain only two values: zero or infinity. These measures allow only certain types of errors and are important in applications where some mistakes cannot be tolerated. These measures are simpler to analyze, yet display many of the complexities of general measures.