A Study of Universal Coding for Enumerable Discrete Information Structures

可枚举离散信息结构的通用编码研究

• 批准号: 14550351
• 负责人: KOBAYASHI Kingo
• 金额: $ 2.24万
• 依托单位: The University of Electro-Communications
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14550351/
• 关键词: universal code; discrete information structure; binary tree; vector k-ary tree; Young tableaux; low density parity check code; watermark; steganography; k-分木; 算術符号; 情報源変換; 落し戸通信路; κ分木; 一般化カタラン数; パーコレーション; エントロピー; Sum-Product復号; ベルヌイ分岐過程 /

The theme of this research project is on a study of universal coding of enumerative discrete information structures, such as integers, trees, graphs and Young tableaux that frequently appear in the computer science, as well as finite discrete data representing letters of text, sampled quantized voice data, and data of brightness and chroma in pictures.We have completed the analysis of coding of binary trees, and extended our method to k-ary trees and vector k-ary trees, the use of which should be powerful for universal coding. Furthermore, we moved a step towards the study of Young tableaux containing the class of trees as a subset of them. We can correspond a binary tree to a 2 x n rectangular Young tableaux. But we cannot correspond k-ary tree and vector k-ary tree to a standard Young tableaux in general. However, we show that by an extended Young tableaux defined by a poset in the integer lattice, it is possible to represent them. These results suggest attractive idea on constructing new code for general trees. Furthermore, we got many aspects on the meaning of Hook formula and the bumping algorithm by generalizing the standard Young tableaux to multi-dimensional tableaux. We presented these results at several international conference(IEEE ISIT 2002,2004,ISITA2004 at Parma, Conferences on General information transfer and combinatorics at Bielefeld university).As well as the above theoretical study, we researched experimentally the performance of watermark and steganography. In the study of watermark for copyright protection and steganography that is considered as a generalized version of hiding information, we performed experiments with respect to the fundamental efficiencies of watermark on resistance against coalition, and steganography using frequency region by considering the structure of relevant data.

该研究项目的主题是研究计算机科学中经常出现的枚举离散信息结构的通用编码，例如整数、树、图和Young tableaux，以及表示文本字母的有限离散数据，采样量化我们已经完成了二叉树编码的分析，并将我们的方法扩展到k叉树和向量k叉树，其使用对于通用编码来说应该是强大的。此外，我们朝着包含树类作为其子集的 Young 场景的研究迈出了一步。我们可以将二叉树对应于 2 x n 的矩形 Young 画面。但我们不能将 k 叉树和向量 k 叉树与一般的标准 Young 画面对应起来。然而，我们表明，通过由整数格中的偏序集定义的扩展杨氏画面，可以表示它们。这些结果提出了为通用树构建新代码的有吸引力的想法。此外，通过将标准Young画面推广到多维画面，我们得到了Hook公式和碰撞算法的多方面含义。我们在多个国际会议（IEEE ISIT 2002、2004、ISITA2004 at Parma、Conferences on General information transfer and Combinatorics at Bielefeld University）上展示了这些结果。除了上述理论研究之外，我们还对水印和隐写术的性能进行了实验研究。在版权保护水印和隐写术（被认为是隐藏信息的广义版本）的研究中，我们对水印抵抗联盟的基本效率以及考虑相关数据结构的使用频域的隐写术进行了实验。

项目成果

修正プライム系列符号を用いたLDPC符号の性能評価

使用修改素数序列码的 LDPC 码性能评估

• 发表时间: 2003
• 作者: 山本裕一

A Survey on Coding of Trees

树木编码调查

• 发表时间: 2002
• 作者: K.Kobayashi; H.Morita; M.Hoshi
• 通讯作者: M.Hoshi

K.Kobayashi: "When the entropy function appears in the residue"Abstracts of Preparatory Meeting of General Theory of Information Transfer. 38 (2002)

K.Kobayashi：“当熵函数出现在残差中时”信息传递一般理论筹备会议摘要。

FFT based sum product decoding algorithm of LDPC coder for GF(q)

基于 FFT 的 GF(q) LDPC 编码器和积解码算法

• DOI: 10.1109/et2ecn.2014.7044980
• 发表时间: 2014-12-01
• 期刊: 2014 2nd International Conference on Emerging Technology Trends in Electronics, Communication and Networking
• 作者: J. Patel;Neeta Chapatwala;Mrugesh P Patel
• 通讯作者: Mrugesh P Patel

Interval Algorithm, Arithmetic Coding, and Shift Operator

区间算法、算术编码和移位运算符

• 发表时间: 2004
• 作者: M.Hoshi; Morita; K.Kobayashi
• 通讯作者: K.Kobayashi