Universal variable-to-fixed (V-F) length coding of $d$-dimensionalexponential family of distributions is considered. We propose an achievablescheme consisting of a dictionary, used to parse the source output stream,making use of the previously-introduced notion of quantized types. Thequantized type class of a sequence is based on partitioning the space ofminimal sufficient statistics into cuboids. Our proposed dictionary consists ofsequences in the boundaries of transition from low to high quantized type classsize. We derive the asymptotics of the $\epsilon$-coding rate of our codingscheme for large enough dictionaries. In particular, we show that thethird-order coding rate of our scheme is $H\frac{d}{2}\frac{\log\log M}{\logM}$, where $H$ is the entropy of the source and $M$ is the dictionary size. Wefurther provide a converse, showing that this rate is optimal up to thethird-order term.
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机译：考虑了$ d $维指数分布族的通用可变到固定（V-F）长度编码。我们提出了一个由字典组成的可实现方案，该字典用于解析源输出流，并利用先前引入的量化类型概念。序列的量化类型类别基于将最小充分统计量的空间划分为长方体。我们提出的字典由从低量化类型类大小到高量化类型类大小的过渡边界中的序列组成。对于足够大的字典，我们得出编码方案的\ε编码速率的渐近性。特别是，我们证明了该方案的三阶编码率为$ H \ frac {d} {2} \ frac {\ log \ log M} {\ logM} $，其中$ H $是源的熵$ M $是字典的大小。我们进一步提供了一个相反的结论，表明该速率在三阶项之前是最佳的。
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