the quantitative theory of information - the institute for logic

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Page 1: The Quantitative Theory of Information - The Institute for Logic

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1212 7"&''+'84 9,#&:;(",+%<"2 ;2/**,*F5 (GHI 9/93- J=>KL M# ./023./0E1=/8 023,-4 ,+ =,..?*1=/01,*N ./-O5 023 :1-02 ,+ .,63-* 1*+,-./01,* 023,-4@ )01..361/0384 =/?>20 023 1*03-350 ,+ 3*>1*33-5C ./023./01=1/*5 /*6 ,023- 5=13*01505@P/0?-/884C ,*3 2/6 593=?8/036 :3+,-3 ;2/**,* /:,?0 023 */0?-3 ,+ 1*+,-./01,* :?0./1*84 /0 023 D?/810/0173 83738@ $-3=153 /*6 <16384 /9981=/:83 *,01,*5 /*6 0,,85 616*,0 3Q150 :3+,-3 ;2/**,*@

;2/**,* +,=?536 ,* 3*>1*33-1*>E0493 9-,:83.5 ,+ =,..?*1=/01,*@ R3=/?53 ,+023 >-3/0 1.9/=0 +,- 023 3=,*,.4C 0215 15 <23-3 023 ./1* 1*03-350 +-,. 5,=1304 8135@R?0 1*+,-./01,* 023,-4 =/90?-35 +?*6/.3*0/8 /593=05 ,+ ./*4 ,023- 923*,.3*//*6 2/5 1.981=/01,*5 /0 023 9218,5,921=/8 83738 -3>/-61*> ,?- ?*63-50/*61*> ,+ 023<,-86 ,+ <21=2 <3 /-3 / 9/-0@ S,-3 /998136 /-3/5 1*=8?63 023 1*03--38/036 T38656*))9-16(%1*- %;$*&"7 6*.1-2 %;$*&"7 ,12-(0 (-(0",1, /*6 6&"4%*2&(4;"@

12?2 @+A)'<2 )*+,-./01,* 15 /8</45 1-:*&)(%1*- (<*9% ,*)$%;1-2@ %23 .$=,6&14%1*- ,+ 1*+,-./01,* .?50 :3 61501*>?15236 +-,. 0215 M5,.3021*>NC A?50 /5 023<,-65 ?536 0, 635=-1:3 / 6,> /-3 61U3-3*0 +-,. 023 6,> 10538+@ V35=-1901,* ,+ 1*E+,-./01,* 1* 9-3=153 03=2*1=/8 03-.5 15 1.9,-0/*0 51*=3C 1* ;2/**,*F5 <,-65 10 <188/88,< >&$4&*.961-2 (% *-$ 4*1-% $1%;$& $?(6%0" *& (44&*?1)(%$0" ( )$,,(2$ ,$0$6%$.(% (-*%;$& 4*1-%@@ %23 635=-1901,*5 1* 1*+,-./01,* 023,-4 /-3 =/8836 6*.$,@

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Page 2: The Quantitative Theory of Information - The Institute for Logic

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%23 03-. M:10N 15 ?536 1* 0<, </45C /5 / -/023- 8,,53 -3+3-3*=3 0, ! ,- "b/5 /:,73c /*6 023*C /5 / .,-3 9-3=15384 63T*36 9-1% *: 1-:*&)(%1*-L C <1% 1,%;$ )(?1)(0 ()*9-% *: 1-:*&)(%1*- "*9 6(- *<%(1- :&*) ( "$,D-* E9$,%1*- @ %,=8/-1+4C =,*5163- D?3501,*5 9,536 /5 /:,73 :?0 <102 -3593=0 0, / .,61T36 =,63E:,,O<23-3 ((C 023 =,63E<,-6 +,- !C 15 -398/=36 :4 (((@ )+ 023 0<, T-50 D?3501,*5 /-3:,02 /*5<3-36 :4 M435NC 023*C /==,-61*> 0, 023 *3< =,63E:,,OC 4,? 52,?86 /5O/ *3< D?3501,* <21=2 4,? =/* ,+ =,?-53 6,C :?0 10 >1735 *, +?-023- 1*+,-./01,*/5 4,? /8-3/64 O*,< 02/0 023 /=0?/8 83003- .?50 :3 !@ %23 63T*101,* 9,1*05 0,=8/551=/8 8,>1= <102 105 -3+3-3*=3 0, M435X*,N b,- M""!N ,- M0-?3X+/853Nc@ )* ;3=01,*(@[ <3 52/88 +,88,< ?9 <102 / .,-3 9-3=153 ./023./01=/8 0-3/0.3*0 ,+ 023 =,*=3905d()*9-% *: 1-:*&)(%1*-d@

%, 3*5?-3 ?*/.:1>?,?5 163*01T=/01,*C <3 -3D?1-3 02/0 / =,63 15 4&$F?=:&$$C 1@3@*, =,63E<,-6 1* 023 =,63E:,,O 15 /88,<36 0, :3 023 :3>1**1*> ,+ /*,023-@ V3*,01*>=,63E<,-6 83*>025 :4 #! $ % ! !$ G&(:%H, 1-$E9(01%"

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.?50 2,86 Z 1*6336C 023 :1*/-4 5?:1*03-7/85 ,+ 023 ?*10 1*03-7/8 02/0 =,--359,*6C71/ 5?==355173 :153=01,*5C 0, 023 7/-1,?5 =,63E<,-65 .?50 :3 9/1-<153 615A,1*0C 23*=32/73 0,0/8 83*>02 /0 .,50 (@ #*6C 1* 023 ,023- 61-3=01,*C 1+ *?.:3-5 #! /-3 >173*5/015+41*> b(@(c 023* 023-3 3Q1505 / 9-3TQE+-33 =,63 <102 023 9-35=-1:36 #!F5 /5 =,63E<,-6 83*>025@

e3 ./4 3Q9-355 f-/+0F5 1*3D?/8104 61U3-3*084C /5 023 9-,93-04 02/0 /*4 83*>02+?*=01,* % " #! .?50 5/015+4 023 8,<3- :,?*6 -350-1=01,*

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%23 =/53 ,+ 3D?/8104 1* b(@(c =,--359,*65 0, 6*)40$%$ 6*.$,C 1@3@ =,635 <23-3 *,=,63E<,-6 =/* :3 /6636 0, 023 =,63E:,,O <102,?0 :-3/O1*> 023 9-3TQE+-33 9-,93-04@

# >?161*> 9-1*=1983 15 0, 6351>* =,635 02/0 /=21373 3g=13*0 6*)4&$,,1*-C 1@3@<21=2 2/73 /5 52,-0 =,63E<,-6 83*>025 /5 9,551:83C ?*63-50,,6 1* 5,.3 /99-,9-1/03</4@ V351>* =-103-1/ 6393*6 ,* 023 0493 ,+ O*,<836>3 ,*3 2/5 /:,?0 023 5,?-=3@)+C 1* 023 3Q/.983C <3 /=0?/884 O*,< *,021*> /:,?0 023 5,?-=3C 023* M.1*1./QN 15/ 5?10/:83 6351>* =-103-1,* b/*6 023 =,63 1* %/:83 ( 15 *,0 ,901./8 /5 10 15 3/54 0,6351>* / =,63 <102 ./Q1./8 =,63E<,-6 83*>025 3D?/8 0, [ -/023- 02/* Hc@

!,*5163- /*,023- 3Q0-3.3 <23-3 73-4 630/1836 O*,<836>3 /:,?0 023 5,?-=3 15/7/18/:83@ e3 2/73 =2,53* 0, 8,,O /0 !2/-835 V1=O3*5F M# %/83 ,+ %<, !10135N@ )0

Page 3: The Quantitative Theory of Information - The Institute for Logic

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(+(&C J >K=2L?M 1NN O 0#&' J >2NN 0#&' J L21P H J L21M!"#$% (' ;0/01501=5 ,+ 83003-5 1* d# %/83 ,+ %<, !10135d /*6 0<, =,63:,,O5@

>3*3-/035 1*61716?/8 83003-5C 59/=35C 9?*=0?/01,* ./-O5 30=@ %, 51.981+4C <3 1>*,-3023 T*3- 630/185 /*6 ,*84 9/4 /003*01,* 0, 023 50/*6/-6 83003-5@ e3 ./4 023*5?../-1l3 ,?- O*,<836>3 /:,?0 023 5,?-=3 :4 81501*> 023 +-3D?3*=135 ,+ 83003-5C =+@%/:83 `@ )0 =/* :3 9-,736 02/0 023 =,63 815036 1* 023 0/:83 /5 / '9I)(- 6*.$ 15,901./8 1* 023 53*53 02/0 10 -3D?1-35 023 5./88350 *?.:3- ,+ :105 0, $-6*.$ 023 3*01-3*,738@ %215 5./88350 *?.:3- 15 `@HHH@`h[ :105 ,- 1* /73-/>3 H@(G :105 +,- 3/=2 ,+ 023hI[@H`j 83003-5@

e3 50-355 02/0 /:,73 <3 2/73 ,*84 /1.36 /0 3g=13*0 =,61*> ,+ 51*>83 83003-5@ W?-5?==355 1* =,.9-3551,* =/* 023* :3 3Q9-35536 :4 023 ,*3 *?.:3- H@(G b:105X83003-c@e3 =/* /85, =,*5163- 023 ,901./8 =,63 /5 / &$:$&$-6$ 6*.$ /*6 .3/5?-3 023 93-E+,-./*=3 ,+ ,023- =,635 1* -38/01,* 0, 10@ B,- 1*50/*=3C +,- 023 F?$. 0$-2%; 6*.$<21=2 15 /85, 52,<* 1* %/:83 `C 023-3 15 / &$.9-.(-6" ,+ a@I( :105X83003-C 3Q9-355E1*> 02/0 02353 :105 /-3 5?93-m?,?5 <23* <3 =,.9/-3 <102 023 ,901./884 /=2137/:83=,.9-3551,*@

%23 510?/01,* =,?86 /85, :3 02/0 ,-1>1*/884C :3+,-3 <3 2/6 630/1836 O*,<836>3/:,?0 023 50/01501=5 ,+ 023 83003-5 1* 023 *,738C <3 ?536 023 TQ36 83*>02 =,63 /*6

Page 4: The Quantitative Theory of Information - The Institute for Logic

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023* 023 -36?*6/*=4 03885 ?5 2,< .?=2 <3 =/* 5/73 :4 5<10=21*> 0, /* ,901./8=,63 ,*=3 <3 2/73 ,:0/1*36 .,-3 630/1836 O*,<836>3@

)+ <3 =,63 023 3*01-3 *,738 ?51*> 023 ,901./8 =,63 1* %/:83 `C 023 =,636 50-1*>50/-05 ,U <102

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<21=2 15 .$6*.$. /5 M10</5023:350,+01.35N =,--359,*61*> 0, 023 ,93*1*> <,-65 1*V1=O3*5F *,738@

e2/0 <3 2/73 =,*5163-36 /:,73 15 -*1,$0$,, 6*.1-2@ )+C 2,<373-C 3--,-5 =/*,==?-C ./*4 *3< 9-,:83.5 0?-* ?9@ B,- 1*50/*=3C 1+ 023 (G02 :10 b!c /*6 023 h`*6:10 b"c 1* 023 /:,73 50-1*> /-3 0-/*5.10036 1*=,--3=084C 63=,61*> 83/65 0, 023 50-1*>M10</813-+0080,01.35N <102 /* 1--10/01*> 93-1,6 ,?0 ,+ 54*=2-,*1l/01,*@ e3 -3/81l3023 *336 0, 63738,9 0,,85 +,- .$%$6%1*- /*6 6*&&$6%1*- ,+ 3--,-5@ %23-3 15 / 2?>38103-/0?-3 ,* 02353 /593=05@ "3-3 <3 ,*84 *,03 02/0 5,.3 -36?*6/*=4 15 *33636 0,9-373*0 =,--?901,* ,+ 023 <2,83 .355/>3 =/?536 :4 / +3< /==163*0/8 3--,-5@ )*6336C1+ <3 ?53 023 TQ36 83*>02 =,63 ,+ %/:83 ` 1*503/6 ,+ 023 ,901./8 =,63C <3 /-3 .?=2:3003- 9-,03=036 />/1*50 ,==/51,*/8 :10 m19 3--,-5@

!,61*> 15 9/-084 ,+ / =,.:1*/0,-1/8 */0?-3 6?3 0, 023 -3D?1-3.3*0 ,+ 1*03>3-5 /5=,63E<,-6 83*>025@ B,- 023,-301=/8 615=?551,*5 10 15 6351-/:83 0, 0/O3 023 =,.:1*/0,E-1/8 61.3*51,* ,?0 ,+ =,61*>@ %215 =/* :3 6,*3 :4 /88,<1*> /-:10-/-4 -3/8 *?.:3-5/5 =,63E<,-6 83*>025@ e3 023-3+,-3 63T*3 /* 1.$(01J$. 6*.$ *8$& %;$ (04;(<$% ! /5 /./9 % " #! ,+ ! 1*0, 023 9,510173 -3/8 *?.:3-5 5?=2 02/0 G&(:%H, 1-$E9(01%" 2,865C1@3@ 5?=2 02/0

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%23 #!F5 /-3 02,?>20 ,+ /5 =,63E<,-6 83*>025 /*6 023 163/81l/01,* 8135 1* /==3901*>/-:10-/-4 -3/8 7/8?35 +,- 023 #!F5@ )+ 3D?/8104 2,865 1* )*3D?/8104 (@[ 023* 023 =,63 155/16 0, :3 6*)4(6%@ #99/-3*084C 023-3 15 / ,*3E0,E,*3 -38/01,*5219 :30<33* =,.9/=0=,635 /*6 9-,:/:18104 6150-1:?01,*5@ )0 15 >173* :4 023 +,-.?8/5

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e23* 02353 +,-.?8/5 2,86C <3 5/4 02/0 023 =,63 ) 15 (.(4%$. %* ' ,- 02/0 ' )(%6;$,)(

e3 =/* 023* =,*5163- *4%1)(0 1.$(01J$. 6*.$,C 1* /*/8,>4 <102 023 *,01,* ,+,-61*/-4 b=,.:1*/0,-1/8c ,901./8 =,635@ )0 0?-*5 ,?0 02/0 /* ,901./8 163/81l36=,63 15 ?*1D?3@ B,- 023 3Q/.983 =2,53*C 023 163/81l36 =,63 52,<* 1* %/:83 ` 1*0<,E63=1./8 9-3=151,* 15 1* +/=0 023 ,901./8 ,*3@ )+ <3 ?53 0215 =,63C /*6 /==390023 1*03-9-30/01,* /5 83*>025 ,+ 163/81l36 =,63E<,-65C <3 52,?86 ?53 `@H`j@i[GC(a:105 0, 3*=,63 023 3*01-3 *,738@ )+ <3 /88,< 163/81l36 =,61*>C 023 93-+,-./*=3 ,+,023- =,635 52,?86 :3 .3/5?-36 -38/0173 0, 023 ,901./8 163/81l36 =,63@ "3*=3 023-36?*6/*=4 ,+ 023 TQ36 83*>02 =,63 1* %/:83 ` 52,?86 :3 a@IH -/023- 02/* a@I(:105X83003- /*6 023 -36?*6/*=4 ,+ 023 "?U./* =,63 15 a@a[ :105X83003-@

12=2 Q'(,+6-2 )0 15 03.901*> 0, 021*O ,+ 023 -38/0173 +-3D?3*=135 1* %/:83 `/5 63T*1*> / 9-,:/:18104 6150-1:?01,* ,73- 023 `jE83003- /892/:30@ #*6 1* ./*4510?/01,*5C 31023- 023 53001*> 15 1*0-1*51=/884 9-,:/:181501= 1* */0?-3 ,- 3853 ./4 :3=,*=31736 /5 :31*> 5,@ #55?.3 023-3+,-3C 02/0 <3 =,*5163- / 5,?-=3 >3*3-/01*>54.:,85 ,73- /* /892/:30 ! /==,-61*> 0, / O*,<* 9-,:/:18104 6150-1:?01,* ' '

Page 5: The Quantitative Theory of Information - The Institute for Logic

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%23 163/81l/01,* 1* %23,-3. ( 15 / >-3/0 =,*73*13*=3 /*6 *, 53-1,?5 -350-1=01,*@%, 3.92/51l3 0215C 830 ?5 1*5150C +,- / .,.3*0C 0, ?53 =,635 <102 1*03>3- 83*>025@%23* <3 =/* =2,,53 =,63E83*>025 #! =8,53 0, $ $%& &! /*6 3*5?-3 1* 0215 </4 02/0*(' ) "

"&!#! + *(' )."@ S,-3,73-C 1+ <3 =,*5163- / 5,?-=3 >3*3-/01*> 53D?3*=35

,+ 83003-5 1*6393*63*084 /==,-61*> 0, 023 6150-1:?01,* ' C 023* 023 .1*1.?. /73-/>3=,63E<,-6 83*>02 93- 83003- <23* <3 =,*5163- 8,*>3- /*6 8,*>3- 53D?3*=35 ,+ 83003-5=,*73->35 0, *(' )@

W+03*C 3*0-,94 15 .3/5?-36 1* -(%9&(0 9-1%, bM*/05Nc -/023- 02/* 1* :105@ )*b(@jc 023*C $%&! 52,?86 :3 -398/=36 :4 $- /*6 3Q9,*3*01/01,* 52,?86 :3 <102 -3593=00, , -/023- 02/* #@ !83/-84C * 1* */05 3D?/85 * 1* :105 .?80198136 :4 $- # % !(/01"@

12L2 R)*#,<#'5# &'A ,#A%'A&'5-2 #55?.3 02/0 4,? ?53 /* 163/81l36 =,63) <102 =,63E<,-6 83*>025 #! * % ! ! 0, -39-353*0 6/0/ :?0 -3/81l3 Z 6?3 0, *3<1*+,-./01,* ,:0/1*36 ,- ,023-<153 Z 02/0 10 15 :3003- 0, =2/*>3 0, /*,023- 163/81l36=,63C )

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Page 7: The Quantitative Theory of Information - The Institute for Logic

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Page 8: The Quantitative Theory of Information - The Institute for Logic

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Page 10: The Quantitative Theory of Information - The Institute for Logic

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Page 11: The Quantitative Theory of Information - The Institute for Logic

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Page 13: The Quantitative Theory of Information - The Institute for Logic

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Page 14: The Quantitative Theory of Information - The Institute for Logic

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Page 15: The Quantitative Theory of Information - The Institute for Logic

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Page 16: The Quantitative Theory of Information - The Institute for Logic

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Page 17: The Quantitative Theory of Information - The Institute for Logic

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Page 18: The Quantitative Theory of Information - The Institute for Logic

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Page 20: The Quantitative Theory of Information - The Institute for Logic

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Page 21: The Quantitative Theory of Information - The Institute for Logic

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Page 22: The Quantitative Theory of Information - The Institute for Logic

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Page 23: The Quantitative Theory of Information - The Institute for Logic

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Page 30: The Quantitative Theory of Information - The Institute for Logic

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)0 0?-*5 ,?0 02/0 023 -3930101,* =,63 15 1*3g=13*0 3Q=390 1+ 023 =/9/=104 15 73-45./88@ )0 /85, 0?-*5 ,?0 02/0 +336:/=O 6,35 *,0 1*=-3/53 =/9/=104@ W*3 ./4 /5O <2402353 =,635 /-3 5, <16384 ?536 <23* 0234C /==,-61*> 0, 023 T-50 ./1* 023,-3. ,+1*+,-./01,* 023,-4C /-3 1*3g=13*0@ #=0?/884C ;2/**,*E0493 =,61*> 6,35 *,0 533.0, :3 ?536 /.,*> 2?./*5 ,- /*1./85@ )*503/6 .?=2 .,-3 9-1.10173 =,635 /-3 ?536@%23-3 /-3C /99/-3*084C 5373-/8 -3/5,*5 +,- 0215@

%23 T-50 15 02/0 3g=13*0 =,61*> 15 =,.981=/036@ %2?5 3g=13*0 =,61*> 5=23.35<188 ,*84 37,873 1+ 023-3 15 / 21>2 5383=0173 9-355?-3 ,* 3g=13*0 =,..?*1=/01,*@W+03* 023-3 15 / 21>2 5383=0173 9-355?-3 ,* >3001*> 023 .355/>3 /=-,55C :?0 1+ 0230-/*5.1551,* =,50 15 8,< 023-3 15 *, -3/5,* 0, 63738,9 5,921501=/036 =,61*> 5=23.35@)0 15 O*,<* 02/0 023 51.983 =,61*> 5=23.35 /-3 3g=13*0 1* / 73-4 *,154 3*71-,*.3*0C5, 1+ 023-3 15 ?*=3-0/1*04 /:,?0 023 /=0?/8 *,153 83738 10 ./4 :3 :3003- 0, :3 ,* 0235/+3 5163 /*6 0-/*5.10 d0,, .?=2d@

%23 2?./* 8/*>?/>3 15 21>284 50-?=0?-36@ )* 8,>1=C 53./*01=5 /*6 81*>?1501=5,*3 50?6135 023 -38/01,* :30<33* 023 .,-3 +,-./8 50-?=0?-35 1*5163 023 8/*>?/>3/*6 023 <,-86 ,?05163 023 8/*>?/>3@ S/*4 >-/../01=/8 50-?=0?-35 <,-O 0, 5,.33Q03*0 /5 / O1*6 ,+ 3--,- =,--3=01,* 1* 023 8/*>?/>3 b:?0 ./4 2/73 ,023- +?*=01,*5/5 <388c@ R?0 <3 O*,< 02/0 10 15 73-4 2/-6 0, 83/-* / 8/*>?/>3 <102 / =,.981=/036>-/../-@ )+ 023 8/*>?/>3 ?536 5,.3 ,+ 023 =,61*> 03=2*1D?35 ?536 :4 3*>1*33-5C /8,0 ,+ *3< d>-/../01=/8 -?835d 2/6 0, :3 1*0-,6?=36@ )* / 53*03*=3 81O3 d%23 ./*2/5 / :,Qd 023 <,-6 d./*d =/* :3 -398/=36 <102 d<,./*dC d:,4dC d>1-8dC d+-13*6d30=@ /*6 023 <,-6 d:,Qd =/*C 1*6393*63*084C :3 -398/=36 :4 d:/88dC d93*dC d501=Od30=@ &/=2 ,+ 023 53*03*=35 <,?86 ./O3 53*53 /*6 =,--359,*6 0, / 5=3*/-1, <21=2 150-?3 ,- +/853C 9,551:83 ,- 1.9,551:83C 9-,:/:83 ,- 1.9-,:/:83@ )* ,?- 51.983 3Q/.983023 53*03*=3 ./4 :3 =,.9-35536 0, d./* :,Qd /*6 <3 =/* 50188 -398/=3 023 <,-65/*6 -3=,73- 023 ,-1>1*/8 50-?=0?-3@ )+ 023 53*03*=3 </5 =,636 ?51*> ;2/**,* =,61*>023-3 <,?86 *,0 :3 023 5/.3 9,551:18104 ,+ -350-?=0?-1*> 023 53*03*=3C :3=/?53 3--,-=,--3=01*> =,635 1*0-,6?=3 6393*63*=135 <21=2 <3-3 *,0 023-3 :3+,-3@ )* 0215 53*53L

X(%( 6*)4&$,,1*- $)4;(,1J$ ,%&96%9&$7 (-. 6;(--$0 6*.1-2 ,)9.2$, ,%&96%9&$M

L2=2 !,&'40)44)+' +. E%&'(%0 )'.+,0&()+'2 %23 O34 0, 023 5?==355 ,+;2/**,*F5 023,-4 8135 0, / >-3/0 3Q03*0 1* 023 D?/*010/0173 -35?805 -3>/-61*> 9,5E51:1810135 +,- +/102+?8 0-/*5.1551,* ,+ =8/551=/8 1*+,-./01,*@ e23* <3 0?-* 0, 02351.18/- 9-,:83.5 -3>/-61*> 0-/*5.1551,* ,+ D?/*0?. 1*+,-./01,*C *3< 923*,.3*/,==?-@ %3=2*1=/884C 10 15 373* 61g=?80 0, >30 50/-036 ,* 023 1*73501>/01,*5 /5 10 15 *,0=83/- <2/0 023 9-,93- *,01,* ,+ / =2/**38 52,?86 :3 1* 023 D?/*0?. 53001*>@ %215=,*=3-*5 D?3501,*5 /:,?0 023 0493 ,+ 1*9?0 /*6 ,?09?0 /88,<36 b=8/551=/8 /*6X,-

Page 33: The Quantitative Theory of Information - The Institute for Logic

h@ S]q%)E];&' !WSS]P)!#%)WP [h

D?/*0?.cC 023 *3=355/-4 /003*01,* 0, 023 2/*681*> ,+ 53D?3*01/8 1*9?0 b<23-3 3*E0/*>83.3*0 2/5 0, :3 0/O3* 1*0, =,*5163-/01,*c /*6 T*/884C 10 =,*=3-*5 D?3501,*5/:,?0 +336:/=O@

!,*5163-1*> 023 7/-1,?5 ,901,*5C ,*3 15 83/6 0, .,-3 02/* 0<3*04 61U3-3*0 04935,+ D?/*0?. =2/**385C /*6 373* +,- 023 51.98350 ,+ 02353C :/51= 9-,93-0135 /-3 *,0 430+?884 63738,936[@ %23 ./*4 9,551:1810135 1*61=/03 02/0 D?/*0?. 1*+,-./01,* 023,-415 *,0 A?50 / 51.983 3Q03*51,* ,+ 023 =8/551=/8 023,-4@ B,- 1*50/*=3C <23* 53*63-/*6 -3=3173- 1* / D?/*0?. =,..?*1=/01,* 52/-3 /* &$'E9/1-C 023*C 02,?>2 0215 1*10538+ =/**,0 :3 ?536 +,- 0-/*5+3- ,+ 1*+,-./01,*C 10 =/* +/=1810/03 5?=2 0-/*5+3- /*6-/153 023 =/9/=104 ,+ 023 =,..?*1=/01,* 54503.@ %21*O1*> /:,?0 10C 5?=2 *3< 9,5E51:1810135 -/153 D?/810/0173 9218,5,921=/8 D?3501,*5 /:,?0 023 */0?-3 ,+ 1*+,-./01,*@P3< 3.3->1*> 163/5C <21=2 /-3 ,*84 9/-084 63738,936 0,6/4C ./4 <388 =2/*>3 ,?-?*63-50/*61*> ,+ 023 73-4 =,*=390 ,+ 1*+,-./01,* 1* -/61=/8 </45@

>2 S%C();%4#, 5+00%')5&()+'

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g=13*0@ %23 ./1* 9-,:83. ,+ .?801E?53- 1*+,-./01,* 023,-4 15 0, T*6 .,-3 3g=13*0 9-,0,=,85 02/* 01.352/-1*>C /*6 0,6303-.1*3 023,-301=/8 :,?*65 ,* 023 3g=13*=4 ,+ 023 9-,0,=,85@ # 593=1/8 3Q/.983,+ / .?801?53- 54503. 15 / =-490,>-/921= 54503. <23-3 #81=3 53*65 / .355/>3 0,R,:C :?0 / 53=,*6 9,03*01/8 -3=3173- 15 &73 <2, <1-30/95 023 54503. ,- 0-135 0,6150?-: 023 .355/>3@

%23 3*>1*33-5 2/73 63738,936 ./*4 53*51:83 9-,0,=,85C :?0 023-3 /-3 ,*84 +3<023,-301=/8 -35?805C 5,C 1* >3*3-/8C 10 15 *,0 O*,<* 1+ 023 9-,0,=,85 /-3 ,901./8@ "3-3<3 52/88 635=-1:3 5,.3 <388 ?*63-50,,6 9-,:83.5 /*6 1*61=/03 023 .,-3 >3*3-/8,*35@ e3 52/88 533 023 O1*6 ,+ -35?805 ,*3 ./4 6-3/. ,+ +,- .,-3 =,.981=/03654503.5@

>212 !"# 0%C()6C# &55#44 5"&''#C2 !,*5163- / *,154 .?801983 /==355 =2/**38<102 0<, 53*63-5@ %23 53*63-5 53*6 7/-1/:835 0 /*6 1 /*6 023 -3=3173- -3=31735 /7/-1/:83 [( %23 =2/**38 15 >173* 1* 023 53*53 02/0 <3 O*,< 023 6150-1:?01,* ,+ [>173* 023 1*9?0 (0$1 ) ( !,*5163- / 593=1T= 1*9?0 6150-1:?01,* ,* (0$1 ) ( e3 /-31*03-35036 1* <21=2 9/1-5 (="$ =!) 2/73 023 9-,93-04 02/0 ;3*63- ( =/* 53*6 /0 -/03=" /*6 ;3*63- ` =/* 53*6 /0 -/03 =!( #55?.3 02/0 ;3*63- ( /*6 023 -3=3173- O*,<51( %23* ;3*63- ( =/* 53*6 1*+,-./01,* /0 / -/03

bh@(c =" " 3 (0*[ ' 1 ) $

[%215 =,*=3-*5C 1* 9/-01=?8/-C 023 5,E=/8836 (..1%181%" 6*-S$6%9&$ -38/036 0, 9-,93-0135 ,+ ,*3,+ 023 *,01,*5 ,+ E9(-%9) 6(4(61%"@

Page 34: The Quantitative Theory of Information - The Institute for Logic

[j (@ %"& \]#P%)%#%)^& %"&W'_ WB )PBW'S#%)WP

R1

R2

time sharing

I(X;Z|Y)

I(Y;Z|X)

-./0+% 8' !/9/=104 -3>1,* ,+ .?801983 /==355 =2/**38@

R1

R2

Slepian-Wolf coding

capasity region

-./0+% 9' )*03-53=01,* ,+ =/9/=104 /*6 =,.9-3551,* -3>1,*@

<21=2 >1735 023 -/03 9/1- (3 (0*[ ' 1 ) $ !) ( )+ 0 15 O*,<* 0, ;3*63- ` /*6 0, 023-3=3173- 023* ;3*63- ` =/* 53*6 1*+,-./01,* /0 / -/03

bh@`c =! " 3 (1 *[ ' 0) $<21=2 >1735 023 -/03 9/1- (!$ 3 (1 *[ ' 0)) ( R4 01.352/-1*>C 023 53*63-5 =/* 53*6/0 -/035 <21=2 /-3 =,.:1*/01,*5 ,+ (3 (0*[ ' 1 ) $ !) /*6 (!$ 3 (1 *[ ' 0))@ R?0 ,*3=/* /=21373 / :3003- 93-+,-./*=3@ )+ 023 0<, 53*63-5 :,02 O*,< 0 /*6 1 0234 =/*53*6 /0 -/03

bh@[c =" .=! " 3 ((0$1 ) *[) (

)0 0?-*5 ,?- 02/0 023 02-33 =,*6101,*5 bh@(cC bh@`c /*6 bh@[c /-3 *3=355/-4 /*65?g=13*0 +,- 023 -/03 9/1- 0, :3 /=2137/:83@

%23-3+,-3C =,--38/036 7/-1/:835 =/* :3 53*0 ,73- / .?801983 /==355 =2/**38 1+ /*6,*84 1+ 023 =,.9-3551,* -3>1,* /*6 023 =/9/=104 -3>1,* 1*03-53=0@ )* ,-63- 0, /=21373/ -/03 9/1- 1* 0215 1*03-53=01,*C 023 5,?-=3 =,61*> 52,?86 :3 /6/9036 0, 023 =2/**38/*6 023 =2/**38 =,61*> 52,?86 :3 /6/9036 0, 023 =,--38/01,*5 1* 023 5,?-=3@ %2?55,?-=3 /*6 =2/**38 =,61*> =/**,0 :3 539/-/036 1* .?801 ?53- 1*+,-./01,* 023,-4@

>2?2 W#(B+,: 5+A)'<2 e3 52/88 50/-0 <102 /* 3Q/.983@ !,*5163- / *30<,-O<102 0<, 53*63-5 4" /*6 4! /*6 0<, -3=3173-5 E" /*6 E! /*6 1*03-.361/03 *,635W /*6 - /5 188?50-/036 1* B1>?-3 G@ #55?.3 02/0 4" </*0 0, 53*6 ,*3 :10 ,+1*+,-./01,* 0, E! /*6 4! </*05 0, 53*6 ,*3 :10 ,+ 1*+,-./01,* 0, E"( #55?.3 02/03/=2 36>3 2/5 =/9/=104 ,*3 :10@ )+ 4" 53*65 23- :10 /8,*> 023 9/02 4"W-E! 023*10 15 *,0 9,551:83 /0 023 5/.3 01.3 +,- 4! 0, 53*6 23- :10 /8,*> 023 9/02 4!W-E"(%23 5,8?01,* 15 02/0 4" 53*65 23- :10 0, E" /*6 W$ /*6 4! 53*65 23- :10 0, E!

Page 35: The Quantitative Theory of Information - The Institute for Logic

h@ S]q%)E];&' !WSS]P)!#%)WP [i

-./0+% :' P30<,-O <23-3 *30<,-O =,61*> ./O35 10 9,551:83 +,-4" 0, 53*6 ,*3 :10 0, E! /*6 +,- 4! 0, 53*6 ,*3 :10 0, E" 02,?>23/=2 ,+ 023 36>35 ,*84 2/5 =/9/=104 ,*3 :10@

/*6 W( %23* W 52,?86 53*6 023 5?. ,+ 023 -3=31736 :105 0, -$ <21=2 52,?86 53*6023 -3=31736 :10 0, E" /*6 E!@ P,<C E" <188 :3 /:83 0, -3=,*50-?=0 023 :10 53*0+-,. 4! +-,. 023 0<, -3=31736 :105 /*6C 51.18/-84C E! <188 :3 /:83 0, -3=,*50-?=0023 .355/>3 53*0 +-,. 4"( %215 15 023 51.98350 3Q/.983 ,+ -$%B*&A 6*.1-2C /*6 </5>173* 1* J1K@

;1*=3 43/- `aaa / 8,0 ,+ -3./-O/:83 -35?805 1* *30<,-O =,61*> 2/73 :33* ,:E0/1*36@ %23 023,-4 <,-O5 <388 /5 8,*> /5 023 *,153 15 :4 638301,*5C 1@3@ / 54.:,8=/* 615/993/- 6?-1*> 0-/*5.1551,*C :?0 10 =/**,0 :3 /803-36@ # 51.983 9-,0,=,8 15,:0/1*36 <23* 3/=2 *,63 0-/*5.105 / -/*6,. .1Q0?-3 ,+ 023 -3=31736 51>*/85@ %23,-1>1*/8 .355/>3 15 -3=,*50-?=036 :4 =,.9/-1*> 023 -3=31736 .1Q36 *,154 51>*/85@)+ 0-/*5.1551,* ,+ / .355/>3 +-,. ,*3 *,63 0, /*,023- 15 9,551:83 :4 /*4 9-,0,=,8C023* 10 15 /85, 9,551:83 <102 0215 51.983 -/*6,. 9-,0,=,8C 1+ 023 0-/*5.1551,* 15 -3E93/036 5?g=13*084 ./*4 01.35@ %2353 *3< -35?805 52,?86 :,02 2/73 9-/=01=/8 /*69218,5,921=/8 1.981=/01,*5@

# -3713< ,+ 023 5?:A3=0 /*6 +?-023- -3+3-3*=35 =/* :3 +,?*6 1* JLNK@

>2=2 3,+&A5&4( 6,+9C#042 )* / :-,/6=/50 54503. 023-3 15 ,*3 53*63- /*6 /*?.:3- ,+ -3=3173-5@ %23 :-,/6=/50 9-,:83. 15 0, 6303-.1*3 023 =/9/=104 -3>1,*C/55?.1*> 023 6150-1:?01,*5 ,+ 023 -3=31736 51>*/85 >173* 023 53*0 51>*/8 /-3 O*,<*@%23-3 <,?86 :3 / 0-3.3*6,?5 *?.:3- ,+ /9981=/01,*5 ,+ 5?=2 / -35?80C /*6 023-3+,-310 15 =,*5163-36 /5 ,*3 ,+ 023 ./A,- ,93* 9-,:83.5 1* 1*+,-./01,* 023,-4@

# 593=1/8 O1*6 ,+ :-,/6=/50 54503. 15 /* 1.$-%1F6(%1*- ,",%$)@ #* 3Q/.98315 =/88E,?05 1* /* /1-9,-0@ %23-3 15 / 593=1/8 .355/>3 +,- / 51*>83 9/553*>3-@ %23593/O3- =/* /66-355 023 .355/>3 0, /88 9/553*>3-5C :?0 0215 15 =83/-84 1*3g=13*0:3=/?53 .,50 9/553*>3-5 /-3 *,0 1*03-35036@ %23-3+,-3 023 593/O3- 50/-05 5/41*>N# .355/>3 +,- S-@ R,: o,2*5,*@@@N #+03- 23/-1*> 0215 1*0-,6?=01,* /88 9/553*>3-53Q=390 R,: o,2*5,* =/* =2,,53 *,0 0, 81503* 0, 023 8/50 9/-0@ %23 593/O3- ./4373* =2,,53 0, 5/4 NS-@ R,: o,2*5,*C 983/53C >, 0, 023 1*+,-./01,* 635ON@ )+023-3 15 / 8,0 ,+ *,153 023 593/O3- ./4 =2,,53 0, -393/0 023 53*03*=3 ,- 1*0-,6?=33--,-E=,--3=01,* :4 5,.3 ,023- .302,6@ %215 15 =/8836 /* 1.$-%1F6(%1*- 4&*<0$)C:3=/?53 023 ./1* 9-,:83. 15 0, 163*01+4 <2, 52,?86 -3=3173 023 .355/>3@ W*3 ./4/->?3 02/0 0215 15 *,0 0-/*5.1551,* ,+ 1*+,-./01,*@ B1-50 ,+ /88 023-3 15 *, .355/>31* 023 ,-61*/-4 53*53@ ;3=,*684 10 15 2/-6 0, =/88 023 9/553*>3- S-5@ #81=3 R-,<*

Page 36: The Quantitative Theory of Information - The Institute for Logic

[I (@ %"& \]#P%)%#%)^& %"&W'_ WB )PBW'S#%)WP

Alice Encryption Channel Decryption Bob

Eve

-./0+% &;' !2/**38 <102 /* 3/7356-,993-@

/ -3=3173-@ #+03- 23/-1*> 023 <,-6 dS-@d 523 O*,<5 02/0 023-3 15 *, -3/5,* 0, 02381503* 0, 023 -350@ %23 510?/01,* 15 5,.301.35 03-.36 1-:*&)(%1*- %&(-,:$& -/023-02/* 1*+,-./01,* 0-/*5.1551,*@

>2L2 @,-6(+<,&6"-2 !,*5163- / =-490,E54503. <23-3 #81=3 </*05 0, 53*6 /.355/>3 0, R,: :?0 /0 023 5/.3 01.3 523 </*05 0, 9-373*0 /* 3/7356-,993- &73+-,. 91=O1*> ?9 023 .355/>3@ %215 =/* 5,.301.35 :3 6,*3 1+ #81=3 /*6 R,: 52/-35/ 53=-30 =,63E<,-6C [$ =/8836 023 A$"@ ]51*> 023 O34 [$ #81=3 3*=-4905 023 40(1-%$?% 0 1*0, / 614;$& %$?% 1(

B,- 0215 0, <,-O =,*5163- 023 +,88,<1*> 02-33 =,*6101,*5Lb(c 0 15 1*6393*63*0 ,+ [$b`c 1 15 6303-.1*36 :4 0 /*6 [$b[c 0 15 6303-.1*36 :4 1 /*6 [(

%23 T-50 =,*6101,* 15 02/0 023 O34 15 =2,53* 1*6393*63*084 ,+ 023 .355/>3 #81=3</*05 0, =,..?*1=/03 0, R,:@ %23 53=,*6 =,*6101,* 15 023 9,551:18104 ,+ 3*=-4901,*/*6 023 021-6 =,*6101,* 15 023 9,551:18104 ,+ 63=-4901,*@

# =-490,E54503. 15 5/16 0, :3 9-6*-.1%1*-(00" ,$69&$ 1+ 0 15 1*6393*63*0 ,+ 1$1@3@ O*,<836>3 ,+ 023 =1923-E03Q0 >1735 *, 1*+,-./01,* /:,?0 023 98/1*E03Q0@

23",4$% (a b%23 ,*3E01.3 9/6c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

%23 ,*3E01.3 9/6 -3D?1-35 73-4 8,*> O345@ )+ / T83 ,+ 51l3 ( r: 2/5 0, :33*=-49036 023 O34 2/5 0, :3 ( r: /5 <388@ W*3 ./4 /5O 1+ / O34 =/* :3 ?536 1* /.,-3 3g=13*0 </4 5?=2 02/0 52,-03- O345 =/* :3 ?536@

/̂-1,?5 1*3D?/810135 =/* :3 63-1736 +-,. 02353 =,*6101,*5@ %23 .,50 1.9,-0/*015 023 +,88,<1*> -35?80L

!)%*+%, ((' /*& (- 9-6*-.1%1*-(00" ,$69&$ 6&"4%* ,",%$)7 * (0) " * ([)B;$&$ 0 .$-*%$, %;$ 40(1- %$?% (-. [ %;$ A$"M

)+ * (0) 15 163*01T36 <102 023 83*>02 ,+ 023 b=,.9-35536c 98/1* 03Q0 /*6 * ([)15 163*01T36 <102 023 83*>02 ,+ 023 b=,.9-35536c O34C <3 533 02/0 023 O34 .?50 :3/0 83/50 /5 8,*> /5 023 98/1*E03Q0 1+ <3 </*0 ?*=,*6101,*/8 53=?-104@ )* 373-46/4 81+3.?=2 52,-03- O345 /*6 9/55<,-65 /-3 ?536@ %23 023,-3. 52,<5 02/0 0234 =/**,0

Page 37: The Quantitative Theory of Information - The Institute for Logic

j@ !WP!q];)WP; [G

Key genrerator

Eve

Alice Bob

Secret channelKey

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