Research on the structure of compact codes for binary memoryless extended sources

这项研究的目的是解决following problems for The compact codes for binarymemoryless extended sources (1) To find out the general form of n，the extension order for a binary memoryless extended source that satisfies the following conditionwhere n is an extension order，k =“n/2”-1，t是任何positive integer.(2) To find out the systematic method To determine theadjacency of two compact codes for a binary memoryless extended source.The results of the研究are as follows:(1) According to the method published on the following Web pages，我们提供了binomial coefficient mentioned is the power of two only in the case that n= 2,6 . 3 and a、http://web2.incl.ne.jp/yaok/nikouks.htm、http://web2.incl.ne.jp/yaoki/anikouks.htm(2)binomial source is obtained by the extension of a binary memoryless source and其属性aredetermined by the extension order and the superior symbol's probability p. As for the enumeratingall Huffman codes for a binomial source我们支持一个code tree modification method based the proposed by Longo and Galasso. Also我们已投资Huffman codes for binomial sources based on some numerical experiments. Inorder to enumerate these Huffman codes for a binomial source of the certain order，we have introduced the concept of index sequence that specifies the sequence of reduced sources inHuffman's procedure. Our numerical experiments have revealed the index sequences and code lengthsets for binomial sources of the order from 2 to 11. the results of the experiments show a coupleof characteristics in the index sequences irrespective of the orders。

The purpose of this research is to solve the following problems for the compact codes for binary memoryless extended sources :(1) To find out the general form of n, the extension order for a binary memoryless extended source that satisfies the following condition :where n is an extension order, k = 「n/2」-1 and t is any positive integer.(2) To find out the systematic method to determine the adjacency of two compact codes for a binary memoryless extended source.The results of the research are as follows :(1) According to the method published on the following Web pages, we proved that the binomial coefficient mentioned above is the power of two only in the case that n = 2, 3 and 6.・http://web2.incl.ne.jp/yaok/nikouks.htm・http://web2.incl.ne.jp/yaoki/anikouks.htm(2) A binomial source is obtained by the extension of a binary memoryless source and its properties are determined by the extension order and the superior symbol's probability p. As for the enumerating all Huffman codes for a binomial source, we have proposed a code tree modification method based the one proposed by Longo and Galasso. Also we have investigated Huffman codes for binomial sources based on some numerical experiments. In order to enumerate these Huffman codes for a binomial source of the certain order, we have introduced the concept of index sequence that specifies the sequence of reduced sources in the Huffman's procedure. Our numerical experiments have revealed the index sequences and code length sets for binomial sources of the order from 2 to 11. The results of the experiments show a couple of characteristics in the index sequences irrespective of the orders.