On information theory parameters of infinite anti-uniform sources

The Optimal Fix-Free Code for Anti-Uniform Sources

“…Compared to the Huffman algorithm, these methods are very complex. A source with n symbols having Huffman code with codelength vector L n = (1, 2, 3, · · · , n − 2, n − 1, n − 1) is called an anti-uniform source [15,16]. Such sources have been shown to correspond to particular probability distributions.…”

“…For example, it was shown in [17] and [18], respectively, that the normalized tail of the Poisson distribution and the geometric distribution with success probability greater than some critical value are anti-uniform sources. It was demonstrated in [15,16] that a source with probability vector…”

Entropy and Average Cost of AUH Codes

“…AUH sources can be generated by several probability distributions. It has been shown that geometric, quasi-geometric, Fibonacci, exponential, Poisson and negative binomial distributions lie in the class of AUH sources for some regimes of their parameters [7], [18], [19], [20]. Related topic was addressed in [21], where the authors studied weakly super increasing (WSI) and partial WSI sources in connection with Fibonacci numbers and golden mean, which appeared extensively in modern science and, in particular, have applications in coding and information theory.…”

M-ary anti-uniform Huffman codes for infinite sources with geometric distribution

“…Tight lower and upper bounds on average codeword length, entropy and redundancy of finite and infinite AUH codes in terms of alphabet size are derived. Related topics are addressed in [13]- [15]. The problem of M-ary Huffman codes is analyzed in [16] and it is shown that for AUH codes, by a proper choice of the source probabilities, the average codeword length can be made closed to unity.…”