任意概率分布下Golomb码和扩展Gamma码的性能分析

以信源的平均值给出了任意概率分布下Golomb码的平均码长的上下界和最优的参数选择准则。在Golomb码的基础上，进一步推广了Elias的码，提出了扩展的码，同时给出了其性能界和最优的参数选择准则。扩展码是一类通用码，而且在一定的条件下可以达到渐近最优的性能。最后，提出了一个低复杂性的基于Golomb码和扩展码的通用数据压缩框架，并通过构建一个样例系统说明了该数据压缩框架的实际应用价值。

Performance Analysis of Golomb Codes and Extended Gamma Codes for Arbitrary Probability Distributions

The upper and lower bounds of the average codeword length of Golomb codes for arbitrary probability distributions as well as an optimal rule for choosing parameters are given in terms of the mean of sources. Furthermore, a class of extended gamma codes which are the generalization of Elias gamma code is constructed based on Golomb codes. The performance bounds and an optimal rule for choosing parameters are also given. Extended gamma codes are universal and can achieve asymptotically optimal performance under some conditions. Finally, a low complexity universal data compression framework based on Golomb codes and extended gamma codes is presented, and a sample system is constructed to indicate the significance of the data compression framework in practice.