准算术惩罚的信源编码
Source Coding for Quasiarithmetic Penalties
摘要：
霍夫曼编码找到一个前缀码，该前缀码对于有限数量的项上的给定概率分布最小化平均码字长度。坎贝尔将霍夫曼问题推广到一类问题，其目标不是最小化平均码字长度，而是最小化称为拟算术或拟线性平均的广义平均值。这样的一般化装置具有许多不同的应用，包括在装配中的应用。几个拟算术平均值问题在广义熵的意义下有新的简单冗余界。一个相关的性质涉及到最佳代码的存在：对于“良好的”成本函数，最佳代码总是存在于具有有限广义熵的（可能是无限字母表）源。解决这些问题的有限实例是通过推广的算法，找到长度有限的二进制代码的一个新的算法，找到最佳的二进制代码的任何quasiarithmetic平均凸成本函数。该算法可以使用二次时间和线性空间来执行，并且可以扩展到其他罚函数，其中一些罚函数可以以类似的空间和时间复杂度来求解，而其他罚函数可以以稍微更大的复杂度来求解。这降低了队列中涉及最小延迟的问题的计算复杂性，允许优化先前考虑的问题的组合，并且极大地扩展了在二次时间和线性空间中可解的问题的空间。该算法可以被扩展用于诸如打破可能不同的最佳代码之间的联系的目的，如底部合并霍夫曼编码。
英文摘要：
Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not mean codeword length but rather a generalized mean known as a quasiarithmetic or quasilinear mean. Such generalized means have a number of diverse applications, including applications in queueing. Several quasiarithmetic-mean problems have novel simple redundancy bounds in terms of a generalized entropy. A related property involves the existence of optimal codes: For ``well-behaved'' cost functions, optimal codes always exist for (possibly infinite-alphabet) sources having finite generalized entropy. Solving finite instances of such problems is done by generalizing an algorithm for finding length-limited binary codes to a new algorithm for finding optimal binary codes for any quasiarithmetic mean with a convex cost function. This algorithm can be performed using quadratic time and linear space, and can be extended to other penalty functions, some of which are solvable with similar space and time complexity, and others of which are solvable with slightly greater complexity. This reduces the computational complexity of a problem involving minimum delay in a queue, allows combinations of previously considered problems to be optimized, and greatly expands the space of problems solvable in quadratic time and linear space. The algorithm can be extended for purposes such as breaking ties among possibly different optimal codes, as with bottom-merge Huffman coding.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
