1. unique! coding for three different motivation flash codes network coding Slepian-Wolf coding test, take-home test

2. recording on write-once media volatile memory... data disappears if power goes out non-volatile memory... data remains even if power goes out non-volatile memory sometimes utilizes non-reversible operation 2

3. write twice on a write once memory 3 0123 0123 (0,1)(1,1)

4. Rivest’s WOM code 4 four bits in three binary cells... one cell has recorded 4/3 bits encoding rule (1st write)(2nd write)

5. flash memory... consists of arrays of flash cells a cell can store electric charge the amount of charge represents the value of a cell a cell value can be raised, but cannot be lowered 5 block erasure; deteriorates cells

6. formalization of the problem 6

7. examples of naive codes 7 420013 250020300071 indexed code ： dispatch small slices in an adaptive manner slices must be accompanied with indices... cells consumed 510300000041000777 777777 320104 index weight

8. ILIFC: Index-Less Indexed Flash Code 8 slice size = data size with a special coding rule, one slice represents two information; the value of a data bit the index of a data bit

9. slice encoding rule 9 1 2 0 1 2 3 d1d1 d2d2 d3d3 d4d4 d5d5 d6d6 00000 2

10. 10 d3d3 is recorded in the slice 000 0 d 3 = 0 000 1 d 3 = 1 000 2 d 3 = 0 000 3 d 3 = 1 001 3 d 3 = 0 d2d2 is recorded in the slice 00 0 0 d 2 = 0 00 0 1 d 2 = 1 00 0 2 d 2 = 0 00 0 3 d 2 = 1 00 1 3 d 2 = 0 slice size = data size a slice is... empty if all cell values are 0 full if all cell values are q – 1 active otherwise 00003333

11. encoding in ILIFC the principle of ILIFC: manage slices so that.... 11 d3d3 d1d1 d4d4 d 1 d 2 d 3 d 4 01 3 010 0 000 0 033 3 333 2 300 0 0 1 0 0 1 01 3 020 0 000 0 033 3 333 2 300 0 0 0 0 0 1 01 3 020 0 000 0 133 3 333 2 300 0 0 0 1

12. summary; flash codes ILIFC is just an example, neither best nor practical studied eagerly in these years constructions of codes analysis of the performance coding theorem 12

13. network coding; problem setting 13 can we do the job?

14. naive answer at a glance, it seems not possible.... 14 remind... information is different from physical objects

15. network coding allow a node to “encode” its input to determine its output 15 coding to optimize the entire data flow over a network ⇒ network coding

16. not a simple story: binary or not binary 16

17. block coding increases the power Regard 00, 01, 10, 11 as 0, 1, 2, 3 in GF(4), respectively: 17 some requirements are achievable with long block some requirements are not achievable for any block length block coding is not almighty

18. basic theorem 18 Rudolf Ahlswede 1935-2010

19. summary: network coding many variations requirements of data transmission numbers and relations of sources/sinks model of the network hyper-graph (wireless communication) dynamically changing (mobile network) applications in sensor networks, distributed storage, etc. asymptotic discussion vs. concrete construction 19

20. Slepian-Wolf coding; problem setting communication with two encoders and one decoder two sources at remote places, possibly correlated encoders cannot see each other’s input 20 Jack Wolf 1935-2011 David Slepian 1923-2007 weather of Osaka weather of Nara

21. source coding theorem 21

22. encoder with “side-information” 22

23. codeword length 23

24. contribution of “side-information” 24 The average codeword length can be reduced if side-information is available.

25. eliminate the side-information 25

26. summary: Slepian-Wolf coding there are many variations of Slepian-Wolf coding. often referred as “Multi-User Information Theory” many problems left unsolved... too difficult! possible applications in mobile communication sensor networks game and gambling 26

27. summary of the course Coding is a bridge between Information Theory and practice. many codes for many different purposes data compression error correction data recording data hiding (cryptography) puzzle and games If you need a “code”, remind that there are many predecessors. 27

28. test course evaluation inquiry （授業評価アンケート） take home test bring a printed copy of your answer to A612 by Dec. 10. answer must be summarized in two pages, make it concise English or Japanese use of books, discussion with your friends... encouraged! 28