摘要翻译：
本文描述了在可数无限字母表上压缩信源的通用无损编码策略。由边际分布上的包络条件定义的无记忆源类为起源于有限字母表上的通用编码理论的编码技术提供了基准。证明了此类源类极大极小后悔的一般上界和极大极小冗余的一般下界。一般上界强调了在无限字母表上下文中，归一化极大似然码对于极大极小遗憾的作用。对于有限字母表上的信源，通过剪裁Krichevsky-Trofimov编码器冗余度的锐界，导出了下界。对于由代数递减（指数消失）包络定义的源类，直到对数（常数）因子，边界都是匹配的。针对由代数消失包络定义的源类集合，描述了有效的和（几乎）自适应的编码技术。这些结果将我们关于通用编码的知识扩展到参数推理的关键工具的上下文中
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英文标题：
《Coding on countably infinite alphabets》
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作者：
St\'ephane Boucheron (PMA), Aur\'elien Garivier (LM-Orsay), Elisabeth
  Gassiat (LM-Orsay)
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  This paper describes universal lossless coding strategies for compressing sources on countably infinite alphabets. Classes of memoryless sources defined by an envelope condition on the marginal distribution provide benchmarks for coding techniques originating from the theory of universal coding over finite alphabets. We prove general upper-bounds on minimax regret and lower-bounds on minimax redundancy for such source classes. The general upper bounds emphasize the role of the Normalized Maximum Likelihood codes with respect to minimax regret in the infinite alphabet context. Lower bounds are derived by tailoring sharp bounds on the redundancy of Krichevsky-Trofimov coders for sources over finite alphabets. Up to logarithmic (resp. constant) factors the bounds are matching for source classes defined by algebraically declining (resp. exponentially vanishing) envelopes. Effective and (almost) adaptive coding techniques are described for the collection of source classes defined by algebraically vanishing envelopes. Those results extend ourknowledge concerning universal coding to contexts where the key tools from parametric inference
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PDF链接：
https://arxiv.org/pdf/801.2456