Universal coding for correlated sources with complementary delivery

Transcription

1 Universal coding for correlated sources with complementary delivery Akisato Kimura, Tomohiko Uyematsu, Shigeaki Kuzuoka Tokyo Institute of Technology NTT Communication Science Laboratories, NTT Corporation Wakayama University

2 Abstract Abstract Universal source coding problem for multiterminal coding system shown below Explicit constructions of universal codes Fixed-length lossless codes Variable-length lossless codes Y X Y encoder decoder 1 decoder 2 X Y X ISIT2007 in Nice, France 2

3 Outline Outline 1. Introduction 2. Preliminaries 3. Code construction 4. Coding theorems 5. Summary ISIT2007 in Nice, France 3

4 Introduction Introduction 1. Introduction 2. Preliminaries 3. Code construction 4. Coding theorems 5. Summary ISIT2007 in Nice, France 4

5 Introduction Introduction Introduction Slepian-Wolf (1973) beginning of multiterminal source coding Csiszar-Korner (1980) first investigated the problem of universal coding for the Slepian-Wolf coding system showed the existence of universal codes Subsequent research mainly focused on the Slepian-Wolf coding system Csiszar (1982), Ahlswede-Dueck (1982),Oohama (1996), Uyematsu (2001) ISIT2007 in Nice, France 5

6 Introduction Main contribution Main contribution Universal source coding problem for another multiterminal coding system Complementary delivery coding system ( broadcast network in the plenary talk by Prof.Effros) Coding theorem was clarified by Csiszar-Korner (1980) Explicit constructions of universal codes Fixed-length codes & variable-length codes Utilize method of types and graph-theoretical techniques. ISIT2007 in Nice, France 6

7 Preliminaries Preliminaries 1. Introduction 2. Preliminaries 3. Code construction 4. Coding theorems 5. Summary ISIT2007 in Nice, France 7

8 Preliminaries Basic definitions (1 /3) Basic definitions Alphabets: Sequences ISIT2007 in Nice, France 8

9 Preliminaries Basic definitions (2 /3) Basic definitions Probability distributions Sources Entropy ISIT2007 in Nice, France 9

10 Preliminaries Basic definitions (3 /3) Basic definitions Types of sequences ISIT2007 in Nice, France 10

11 Preliminaries Previous result Previous result Y X X Y X X = & Y X Y Y X Y ISIT2007 in Nice, France 11

12 Code construction Code construction 1. Introduction 2. Preliminaries 3. Code construction 4. Coding theorems 5. Summary ISIT2007 in Nice, France 12

13 Code construction Code construction (1 /3) Code construction ISIT2007 in Nice, France 13

14 Code construction Code construction (2 /3) Code construction To reproduce all sequence pairs at decoders ISIT2007 in Nice, France 14

15 Code construction Code construction (3 /3) Code construction ISIT2007 in Nice, France 15

16 Code construction Equivalence to graph coloring Equivalence to graph coloring The table can be converted to a bipartite graph Encoding is equivalent to edge coloring of the bipartite graph row column ISIT2007 in Nice, France 16

17 Code construction Necessary number of symbols Necessary number of symbols ISIT2007 in Nice, France 17

18 Code construction Coding scheme Coding scheme Fixed-length coding: Variable-length coding ISIT2007 in Nice, France 18

19 Coding theorems Coding theorems 1. Introduction 2. Preliminaries 3. Code construction 4. Coding theorems 5. Summary ISIT2007 in Nice, France 19

20 Coding theorems Fixed-length Coding theorem Fixed-length coding theorem ISIT2007 in Nice, France 20

21 Coding theorems Variable-length coding theorem Variable-length coding theorem ISIT2007 in Nice, France 21

22 Summary Summary 1. Introduction 2. Preliminaries 3. Code construction 4. Coding theorems 5. Summary ISIT2007 in Nice, France 22

23 Summary Summary Summary Investigated universal coding problem for complementary delivery coding system Presented explicit constructions of universal codes Established a coding theorem for each problem Future work More than 3 messages and/or more than 3 decoders will be presented in the recent result session Practical universal coding schemes Lossy universal coding schemes will be presented in another conference ISIT2007 in Nice, France 23

24 Ends Thank you Thank you very much ISIT2007 in Nice, France 24