Abstract：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.
2005, Vol. 27 
