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

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

write twice on a write once memory (0,1)(1,1)

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

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

formalization of the problem 6

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

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

slice encoding rule d1d1 d2d2 d3d3 d4d4 d5d5 d6d

10 d3d3 is recorded in the slice d 3 = d 3 = d 3 = d 3 = d 3 = 0 d2d2 is recorded in the slice d 2 = d 2 = d 2 = d 2 = 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

encoding in ILIFC the principle of ILIFC: manage slices so that d3d3 d1d1 d4d4 d 1 d 2 d 3 d

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

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

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

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

not a simple story: binary or not binary 16

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

basic theorem 18 Rudolf Ahlswede

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

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 David Slepian weather of Osaka weather of Nara

source coding theorem 21

encoder with “side-information” 22

codeword length 23

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

eliminate the side-information 25

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

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

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