(c)  騭, ᪢

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             ⥫ ଠ樨:   㬠?
             

(".  " 1-3/2004)
ࠢ .

        ࠭ 設-⠥ ଠ樨
ᯮ짮 㬠 ⥫ - 䮪  䮫. 
⤥ ,  ࠭ 讣 ⢠
ଠ樨, 㬠 ᯮ  ᥩ (-).  
࠭  񬮢 ଠ樨 ⥯ ᯮ 
 ᪨ ⥫.   ,  ᯮ짮 㬠
 ⮩ 楫 㦥   ᫠?
        ࠭  㬠 让 
設-⠥ ଠ樨?   , 祭 :
⮢ ࠦ, ᮤঠ饥 㦭 ଠ (ਬ,
 ᥫ - 0,  - 1),    ਭ 
 ࠦ  㬠.   ⥭ ଠ樨 -
ᯮ짮 ᪠.
    ,  . 1   㢨,   ⮬ 㤥
룫拉 ᯮ塞 䠩  ணࠬ Text Corrector, ࠧ
ண - 848 ⮢ (6784 ).  ।⠢  
୮- ࠦ ࠧ஬ 100x68,  ⮬  ⠫
ᯮ㥬 16 ᥫ.

                         Ŀ
                         1.gif       
                                     
                                     
                         
                             . 1

    ᫨, ᪮쪮 ଠ樨 ( )  㬥
  ࠭ ଠ A4 (210x297 ), ᫨ 
ந  ࠧ襭 600 dpi (.. 600 祪   - 
 ࠢ 25,4 ):

                210*297*(600/25,4)^2
                 ~= 4,15 .
                       2^23

    ! ࠢ   ⥬ 񬮬 ଠ樨, 
㬥頥   ࠭   筮,
祫-⠥ :-) ⥪. ਬ,  ⮬ ୠ ࠭
ᮤন ਬ୮ 6000 ᨬ ⥪. ᫨ ,  
ᨬ   ⮬, 稬 6000 ⮢.  
ᯮ짮 襮ᠭ ᯮᮡ  ⮩  ࠭ 
㬥  (4,15*2^20)/6000~=700 ࠧ  ଠ樨.  
,  ⥪  ।⥫쭮 ᦠ: ᫨ , 
 ᦨ   ࠧ, 稬,    ࠭ 
 ଠ, ᮤঠ ਬ୮  2000 ࠭
⥪!
     ,   㯠  㫠? :-)  ⥯ 㬠, 祬
 ⠪ ᯮᮡ ࠭ ଠ樨  ᯮ. 筥 -
, -  ᯮ,    ⮬  ,  
᫨ ⠪,  ࠢ 砥,   ᯮᮡ 
࠭.  ,    ?   ஭, 
ᠬ , 㡫樨   ⥬   .  
㣮 ஭ - ⭮,   ᯮᮡ ᫨誮 祢, ⠪
 猪    뢠   ᯮ짮.
        ? ,   ⮣ ᯮᮡ -
⪨. :-) , -  ⥫   ᯮ짮, 
-  ⪮ ⠫ ᯮᮡ ਣ.  㣮
஭,  , ⠫ 祭묨 - 
⮨⢠.
     饬,  訫   ᢮ ᮮࠦ  
⮣ ᯮᮡ, ᬠਢ   ࠧ ஭.  ,
-   㦤  ,    ⨫
 ,  ࠭   ⮬ .

     ᯮ짮 ᪥, -᪮  㣨 
⥫ ଠ樨, ᫨  - ᠫ  ,  ⮬
  ᠬ  ⠥.  㬠  ⠪. ᥫ ⠭
ࠦ  㤥  筮 ᮮ⢥⢮ ᥫ
⠭ ࠦ - ᮢ . , 
. 2  ࠦ  㢥祭   孨 㣮 . 1,
  . 2  - ࠦ, ஥    
᪠஢. ( ᠬ      ਭ,  ᪠,
⠪   祭 ⮣ ࠦ  諮 
ᯥ樠 ணࠬ,  ⠥ ஢ ᪠,
騥  ᪠஢.)

                     Ŀ Ŀ
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                          )          )
                             . 2

     ࠧ, ⠭  ᪠ ࠦ ਤ
⥫쭮 ࠡ, ⮡  ᠭ ଠ. 
 ⮣  ,   ᪠ ࠦ 
  ᫥饬 ᪠஢,  ࠧࠡ ᯥ樠
, ⠭騩 室 ࠦ.

    ,    娢஢ 室  ।
, ⮡ 㬥  ࠧ.   㤥 祭
஥ ६,   ᮪ 室 㬠  ⥫,
㬥 ६   ᫥饣 ᪠஢ ( ⮣
   먣  ६).

     㯮,     ࠧ襭 600 dpi 
࠭  㬥 4,15  ଠ樨.  ᥣ  
祭 ⨦  ࠪ⨪? 祢, .  , 
, ਭ   ᯮ짮 ᮫⭮  頤
.   ਭ    ᮪ ࠧ襭.
  窨  ᯫ뢠, ⠪   ᫥饬
᪠஢ (  ᮪ ࠧ襭) ࠧ ⠭
㦥  㤠. ᪮ ᨬ쭮 ࠧ襭 
   䠪஢:  ⭮  ਭ, 
ᯮ㥬 㬠,  ᯮ㥬 ୨ ( 㩭
ਭ),  ᯮ㥬 ⮭ ( ୮ ਭ) ,
,   ⥬   . :-) 쪮
ᯥਬ⠫쭮  ஢,   ࠧ襭 
, ࠭ ࠧ稢  ᥫ.

      ࠭ ଠ樨 㬥蠥    ⮩
稭,  㬠 - 筮  ⥫, ⮡
७ 묨 訡   ᯮ짮. ᫨,
ਬ,  㬠  񬭮 誮 -  㤥
 㦥 ᪮쪮 訡 ᥫ.   㬠 
 ० 㦥 ᫥  (ਬ, ᫨   ᫮
 - ᫥⢨  ᪠஢ ᥫ, ᯮ 
ࠩ ᣨ,   ⠭  訡;  ᫨ 
,  ⮬   ஡).
    ⮡ 㦨 訡, ਤ ࠭ ஫
㬬 (CRC) ᠭ .  ᫨  ⨬  
⮬᪨ ࠢ 訡, ਤ ࠭ 
ଠ   ࠢ.   ନ஢ 
 ଠ       ࠢ 
 ଠ樥 - ⤥ , 騩  ⢠
 ࠪ 訡,  । ࠢ.

    த  ⭮,   ࠭祭: ࠧ襭
᪠     ࠧ襭,   뫮
⠭ ࠦ,    ᥫ 砥 
᪠஢ ࠦ 㤥 㬬஢ મ ᪮쪨
ᥫ ⠭ ࠦ,  ⠭ ⠭
ࠦ  .    - ८ 
࠭祭, ⥬ ᠬ ਢ  ਬ 뢠
ᯮᮡ ࠭ ଠ樨?
      (ਬ, ᠭ  [1]), 騥
   ᪮쪨 ࠧ ࠦ -
ꥪ   ࠧ襭 ந १饥
ࠦ ⮣ ꥪ  訬 ࠧ襭.  ࠪ᪮
ࠧࠡ⪥  ⮩  ᪠뢠  [2]: ࠡ뢠
᫥⥫쭮 ࠦ  ࠧ襭 32x32, 㤠
 ࠧ襭  㦥, 祬 256x256.
      ⥮᪨ 筮 ᪮쪮 ࠧ 믮
᪠஢   ⮣  ⠭ ࠦ, 
ࠧ  ᤢ  㬠,  ⥬ ࠡ 祭
ࠦ   ⠪ ⬠, ⮡ 
ࠧ襭. ,  . 3     ࠦ
㪢 "A"   ࠧ襭  祭   ᭮
ࠦ   ᮪ ࠧ襭 (  , 
室  ࠦ  稫   १ ॠ쭮
᪠஢,    ᯥ樠쭮 ணࠬ; १饥
ࠦ, 祬, ⭮ 뢠   ).

       Ŀ Ŀ Ŀ Ŀ Ŀ
       3a.gif  3b.gif  3c.gif  3d.gif  3e.gif 
              +       +       +       =       
                                              
           
                             . 3

      ஡ ᪠  ,  㬠 
 -  룮  ࠢ  㣨 ⥫ﬨ
 (᪥, -᪨).

    ࠭   㬠   襢  ࠢ 
᪥⠬ (筮,    塞 , 
᪥ 룮    ୮ ᯮ짮).  ,
 ,     ᪥,    ⠪
㤮   㬠.  ࠩ ,    ⪠
࠭  ᢮ ,   ࠢ⥫쭮 ।
室  (ਬ, 娢 ),  ⠪
ࠧ.

    , ⮨  ଠ樨  㬠 
㬥   ᯮ짮... 㦥 ᯮ짮 㬠!
-!    ?
       㦭  㬠  ⠭  
⥪⮬.  ⮬ 襭,  ࠢ,   
頤 .  ᠭ ਤ  ਭ஢ 筮
㪠뢠,    ⢠ ࠭  墠, 
 5%  ࠭.    ᭮  
 祭.
    , ᫨ ,   ⠥ ࠦ ⢮
   ᥫ ,   2,5% ᥫ
 訡묨.  ᠬ , 訡   
  ᥫ,      㦥 襭
⮪ 㬠  ⮬ ⠫  .  ᫨ 
ᥫ     㦥 襭 ⮪ 㬠, 
 ਢ  訡.
     ࠪ  訡,  ࠧࠡ ଠ 
筮 ଠ樥, 騩 ࠢ  訡.
⢥, 筮 ଠ樨 ਤ  ,
祬    ⮬ , ,   ,  祭
  ࠢ  񬮬  ଠ樨.

    ஡㥬 業 稭 筮 , 室
 ࠢ 訡,     㦥
ᯮ짮 㬠.  ⭮,  ⥮ਨ ଠ樨
뢠,   筮 ஢  ᮮ⢥
।񭭠 稭 筮 ,  室
 筮  ⮣, ⮡ ⭮ ࠢ쭮 
ᮮ饭 뫠  㣮   .
    ⠥,   㥬 ᮮ饭 ஢ 㫥  ,
0   ᥫ,  1 - , ⭮⥫쭮
⢮ 㦥   㬠  ᥫ ࠢ k (..
⭮ ⮣,  ⠥ ᥫ   㦥 騩
 㬠  ᥫ, ࠢ k),   㣨 筨 訡
.
    稭 室 筮  ࠢ 
ଠ樨  । ᮮ饭.  [6]  ଠ樨
砥 Hy(x)  ਢ 㫠   ᫥:

                           
               H (x) = - > p   > p (j) log p (j),
                y        i  i         i
                        (i)   (j)

 p     - ⭮ ਭ ᮮ饭 i,
     i
    p (j) - ᫮ ⭮ ⮣,  뫮 ।
     i      ᮮ饭 j, ᫨ ਭ ᮮ饭 i.

    ᫨  ⢥   ଠ樨 ਭ , 
᭮ 䬠  ⮩ 㫥  ࠢ .

    ᬮਬ  ଠ樨  ।  . 
襬 砥 p0 (⭮  0) 㤥 ࠢ 0,5*(1-k), 
p1 (⭮  1) ࠢ 0,5*(1+k).
    ᫨  ਭ 0 - , 筮  । 0, ..
p0(0)=1  p0(1)=0. ᫨   ਭ 1,  ⭮ ⮣,
  । 0, ࠢ k/(1+k),  ⭮ ⮣,  
। 1, ࠢ 1/(1+k), .. p1(0)=k/(1+k)  p1(1)=1/(1+k).

    Hy(x)=-p0(p0(0)*log2(p0(0))+p0(1)*log2(p0(1)))-
          -p1(p1(1)*log2(p1(1))+p1(0)*log2(p1(0)))=
         =-0,5*(1-k)(1*log2(1)+0*log2(0))-
          -0,5*(1+k)((1/(1+k))*log2(1/(1+k))+
          +(k/(1+k))*log2(k/(1+k)))=
         =-0,5*(log2(1/(1+k))+k*log2(k/(1+k))).

     . 4  ᨬ Hy(x)  k   k 
0  1.

                      Ŀ
                      4.gif               
                                          
                                          
                                          
                                          
                                          
                      
                              . 4

     k=0,05 (..   㬠 㦥  5% 
ᥫ)  ଠ樨  ।   ࠢ
ਬ୮ 0,145 .    ।  
⥮᪨  । 1-0,145=0,855  
ଠ樨 ( 0,145  -  㤥 筠 ଠ,
室  ࠢ 訡  ।). 묨 ᫮,
   筮 ଠ樨 ਤ 㢥
ࠧ ।   1/0,855~=1,17 ࠧ.
    ࠢ, ⥮   ⢥  ,  
ࠧ  ஢ , ⮡ ࠢ  訡 
⠪ ஢ 筮. ⢥ত ,  ⠪ 
.

    ⠪,    㦥 ᯮ짮 㬠 ᢮ 
 室  㬠  ६ 蠥 ஡
⨫樨 ᯮ짮 㬠. :-)  㣮 ஭,  
: ,   㦥 ᯮ짮 㬠 
। -  ਭ?

    த ᪠   २⢠ 㬠.

    ᪥   ⠪ ⥯ ,  ⥫ . 
த    稭 " ⠥"   ᪮쪮
ᥪ஢,  ந室  ଠ樨. ୮,  ᬮ
ᯮ ⠪ 砨.   ࠭ ଠ樨  㬠, 
 ,   襩 񦭮  
⮬᪮  筮 ଠ樨, 饩
⠭ ᠭ     ०.
    ,    ᪥ ⮦   
ଠ (ਬ, 㯠  RAR'  ⠭
ᮮ⢥饩 樥).   ⮬   ᠬ
짮⥫,      ⨬.  ⮬ 
筠 ଠ,   䠩,  , ᫨
- ० ⠫  祭 ଠ 
ᯮ 䠩  ᪥,     㤥 㯠 
䠩.

      -᪮ ॡ 筮 
, ண 騩 ਢ.     ᪠஢
 ᯮ짮 ࠪ᪨   -  ,
 ZX Spectrum.

        -  ᪥ 室
     ᮤন  , ⨪⪥
( אַ  -᪥ ᯥ樠 થ஬), ⮡ 
९,   ᪥  ᠭ.     
㬠 ⥫  ᢥ   ⠭
⮬᪨, ६   ᮤন!
    ࠢ ࠤ ⬥,    -᪮
⠪   ⮬᪨ ନ஢ 
ᯮ㥬  ᪠   
ந쭮 ࠦ  ⥪ (ਬ,  ᠭ
ᮤন ᪠) (. [5]).  ⭮,   㬠 
-⠪ 㤮.

     , - ᪠,   ⠪ 㤮  
᪠஬  ࠢ  ᪥⮩.   ᪠,  ᪠ 
 饬 ⠭ ⠪ ,  ᥩ?  , 
祧  ᠬ⥫쭮 ன⢮,   ᮢ饭 
࠭,  ᠭ  [3].  ਪ뢠  㬠 
࠭ -  ଠ 㦥   !   ,
祬 ⠢ ᪥  ᪮!

     ।⠢ ,   । ଠ
    㣮,  ࠤ樮 ᯮᮡ 
- 稭  室. ਬ, ७ ଠ
 ᪥ , ⮬     ஢ 
᪮; 易  ⥢   
       㣮 - ⠪
 - 稭   㤮.  ⮬ 砥
ᯮ짮 㬠  ⢥ ஬筮 ⥫
ଠ樨   ⢥ 室;  ⮫쪮, ⮡
 뫮  ਭ  -筨 ଠ樨
 ᪠ -  -񬭨.

        ஡ - ࠫ쭮 ७
⥫ ଠ樨  ன  ⥭  ⥫.
  ᥩ    ᪮ 5,25"? ? 
,    ଠ, ᠭ  ⠪
᪥. १ ᪮쪮      
᪥⠬ 3,5": 㦥 ᥩ ந⥫ ᪠ 
  ᪮.  ,   졠  
㣨 ᯮ㥬  饥 ६ ⥫ ଠ樨.
      ⥭ ଠ樨  㬠 ⥫  㦭
 ᯥ樠 ன, ஬ ᪠. , 
饬 ᪠  룫拉  ⠪,  ᥩ ( ,
. [3]),  祧 , -,  
室.
      ᪠  ᥩ  뫮   ᮡ 㤠
 ଠ, ᪠,  䮪.  ⮫쪮 ,
 ࠧ  ଠ 뫠 ஢. ,  
 ଠ樨  㬠  ⮬᪨   ⮬
  㬠   ( ⢥ 祫᪮
몥)  "஢" ⠭ ଠ樨.

    ,   ந  ⨯᪨ ᯮᮡ,
 ⮬   㤥 祭 񢮩.   
, ୠ ਫ -  ᪥,  
⭮ 㤮஦ .   뫮   ଠ 
設-⠥  אַ  , ୠ ( ,  
 ଠ,   ᪥,    ).
, ᫨  ࠦ த  ᪮,   -  ,
㯠⥫ ᠬ ᬮ ,    : 㯨 
 ᪮ ( 㤮 짮,  ஦)   ᪠
(ਤ   ᪠஬,   !).
      , 㡫㥬  ⮬ ୠ,  
ਢ 室 ⥪ ணࠬ - - ᫨誮 讣 
.   뫮    室 ⥪, 
ᯮ塞 䠩  ணࠬ  設-⠥  - 
    ॡ.
    த  ⭮,   ⮬  ࠭ ଠ樨
ॡ ⥫  㬠,  ⠪ 㤮஦
.  ...   ᯮ짮 ⥫쭮 
 ⭮ ᠭ⨬ 㬠    ⥬ ࠭
㦭 ଠ. ?

    ᫨ ⥪ ⠥    䮭,  ଠ 
࠭ ।⢥  䮭 ⥪. ⨬, 䮭  
ᢥ⫮- (50%   50% ⮣).   
ࠢ୮ ।    ᥫ (. 5 )
 ⮣  ⥭, ஢ 室  ⠪,  0
㤥 ।⠢  ᥫ,  1 -  (. 5 ).

                    Ŀ  Ŀ
                    5a.gif     5b.gif   
                                        
                      
                         )           )
                             . 5

     ⮬, ᫨  室  0  1 ᯮ  楫
ࠢ୮ ( ᫨ 室  祭  १
娢樨,  ਬ୮ ⠪  㤥),  稢訩 䮭 
㤥 ⭮ ⫨  室 (᫨   
 ࠢ୮ 梥 䮭, ⥭ ⥪  
蠥).  ⥯  䮭 㦥 ࠭ "" ଠ, 
 ᪠஢  㤥  .
    㬥,  ⮬ ਤ 易⥫쭮 ᯮ짮
 ଠ, ⠪   ᥫ 䮭 ४뢠
ᥫ ⥪,  ஢   ଠ 㤥
ﭠ (祬,   㦥 㯮, ᥫ ⥪ 筮
⠢    ᥩ 頤 ࠭). 㣮
ਠ - ࠭ ,  ᥫ 䮭  ४
⥪⮬,   ᯮ짮   ࠭ ଠ樨,  
᪠஢ ࠧ 㭪樨 ᥫ   梥: ᫨ ᥫ
  ,   ⭮  䮭   ଠ, 
᫨ ᥫ  - ,  ᥫ ⥪ (  
⮫쪮  梥⭮ 䮭).

     砥 ୮- ,  ⥪ ⠥  ஬
䮭, ।⠢饬 ᮡ 㯮冷祭 ᬥ   
ᥫ (. 6),  筮 ⠪   易⥫쭮
㯮冷祭 ᯮ ᥫ 䮭  ᮮ⢥⢨ 
㥬묨 묨 ⠪,  祭 ࠦ 㤥 
⫨稬  室.

                          Ŀ
                          6.gif    
                                   
                          
                            . 6

    ⨬,   ࠦ,   . 6, 
  䮭  ଠ, ⢮ 0  1  ன
ਬ୮ ࠢ   ६蠭 - ࠢ୮.  䮭
ନ㥬 ⠪: ᭠砫  䮭   襩 ⭮
 ᥫ (. 7).

                          Ŀ
                          7.gif    
                                   
                          
                            . 7

     ୮ ᥫ 䮭 ⠢  ᮮ⢥⢨  
㥬 ଠ樨,  ⮬  ᥫ,  ᮮ⢥
㫥 ,   묨,  묨 (. 8).

                          Ŀ
                          8.gif    
                                   
                          
                            . 8

     १ 騩 ⥭ 䮭 ⭮   
ࠢ  . 6, ⠪  ᮮ⭮襭    ᥫ
 । ⠭ ⥬  ᠬ.
     祭 䮭 뢠 ࠦ ⥪
(. 9).

                          Ŀ
                          9.gif    
                                   
                          
                            . 9

       ᯮ짮 䮭  ࠭ 
    ﭨ 㡫樨 [4]. ᫨  ᥫ
䮭, ᯮ  㧫 ॣ୮ ⪨, 室 
筮 讬 ﭨ   㣠 (஬⮪ 
 ᥤ ᥫ  ⨪, ਧ⠫ 
 -    ᥫ),   ᤥ ⠪:
ᤢ   ᥫ 䮭    쬨 ᥤ
ᥫ (. 10)  ⠢   .

                          Ŀ
                          10.gif   
                                   
                          
                            . 10

      ⮬  䮭,   . 11.

                          Ŀ
                          11.gif   
                                   
                          
                            . 11

     ୮ ᥫ 䮭  ᮮ⢥⢮ 
 ਠ⮢  ᯮ.  ࠧ, 
⠪ ᥫ 㤥  log2(9)~=3,17  ଠ樨.
     ⮬   ᯥ稢  த 䮭
(⢨  ᢥ   ⪮),  
  ஢, - ⮬  ⢮  ᥫ
 ,   ⮫쪮  न,   
祬  1   ࠢ.
    ᫨ 室 ﭨ  묨 ᥫ 䮭 
 ᥫ,   ᤢ ᥫ    稭.
 ⮬   ᥫ 㤥    ,
ᮮ⢥⢥,  㤥   ଠ樨.

     ஡㥬 ᬮ    ஡.
  ⠥ :  0 ।⠢  (襭)
ᥫ,  1 -  (襭). ᫨  ᠬ  
室 ⥫ (୨, ⮭,  ), 
砥,   ᥫ 室  ஦ . 
  ⠪ ४஢ , ⮡ 㬥
⢮  ᥫ (    㢥祭
⢠  ᥫ -   襢),  ⠪ ࠧ
᮪ ⮨  .
    ਢ ਬ.   ᥫ ⮨   ࠧ ஦
.    㤥 ,   室 
    ⭮ ࠢ 0  1 (᫨
室  祭  १ 娢樨,  ਬ୮
⠪  㤥).
    ਬ 業  ᥫ  1 .., ⮣ 業 ୮ -
3 ..  । 㫥   ⮫쪮 , ᪮쪮 , 
 筮 ᯮᮡ  業    ⠢
(1+3)/2=2 ..
     ⥯ ४㥬 室 ,   
 ⠪,   :

    00 -> 1
    01 -> 01
    10 -> 001
    11 -> 000

       室   । ஢ 権 00,
01, 10  11,   ।   室 ଠ樨 
஢  (1+2+3+3)/4=2,25 ,   㫥 㤥
(0+1+2+3)/4=1,5,   - (1+1+1+0)/4=0,75.
     । 業   ⮢ 室 ଠ樨
᫥ ४஢ ࠢ 1,5*1+0,75*3=3,75 .. । 業
  , ᮮ⢥⢥,    ࠢ
1,875 . -  ࢮ砫 2 ..
    (,  襮ᠭ ஢  
:   㢨 , ⥮᪨  業
     ᮮ⭮襭 業   ୮
ᥫ ࠢ ਬ୮ 1,81 ..)
    ⠪,     ஡?  ⮬, ⮡ 㧭,  
 ᮮ⭮襭 業   ୮ ᥫ 
४஢ 室 , ⮡ ⮨   뫠
襩.  , 筠 ஡  ᬠਢ
 ⥮ਨ । ଠ樨 (᫨ ६ । 1  
裡  ६ । 0    襣
६ । ).  ଠ樨   襭   
(  - ,  ᪠), ⮬ ਢ ᮡ⢥
ࠧ諥   ⥬.
      ᥫ  k ࠧ ஦  (k>1).  㦥
㯮 , ⠥,   室    
 ⭮ ࠢ 0  1.    訩
()   k ४஢騪 室 , ..
ᯥ稢騩  ।  業   
室 ଠ樨 ᫥ ४஢ (稬  業
C).   ࠡ⠥  ४஢騪,    ,
  ᥩ .
      㫥  ४஢   । ࠢ x
(  ४஢  ࠢ 0  ⭮ x
 ࠢ 1  ⭮ 1-x). 祢,  x>0,5, ⠪ 
㬥 C  ⮫쪮   ⭮⥫쭮 㢥祭
⢠ 㫥  .
     祢,  ࠧ ४஢  㤥 
।  ࠧ 室 .  ᫥  ⮣, 
⢮ ଠ樨 ᫥ ४஢  ࠭,
 ᫨ ᫥ ४஢ 㫥 ⠫  । , 祬
,    ४஢  㤥 ᮤঠ
   ଠ樨,  ,  ࠭ ⮣ 
⢠ ଠ樨,  뫮  室 , 
 ⮢.
    ஡㥬 ᫨ x. । 業   
४஢  (稬  C') ࠢ x*c0+(1-x)*c1,
 c0 - 業  ᥫ, c1 - 業 ୮ ᥫ. 
।, ᪮쪮 ⮢ ४஢   ᮤঠ
⮫쪮  ଠ樨, ᪮쪮  ᮤন   室
 (   ᮤন   ଠ樨).
    ଠ樮 񬪮   ४஢ 
(稬  H) ࠢ -(x*log2(x)+(1-x)log2(1-x)).  x>0,5
H<1.     ଠ樨, ᫥⥫쭮,
ॡ 1/H ⮢ ४஢  ( 
).
     ᪠ ᫥, 
C=C'/H=(x*c0+(1-x)*c1)/-(x*log2(x)+(1-x)log2(1-x)).  
c1/c0=k ( ।), , ᫨ ਭ c0=1 (  㢨
, x    c0), 稬:

                           x+(1-x)*k
               = - .
                    x*log2(x)+(1-x)log2(1-x)

      C 쭠 ( ᫮ ),  । x
筮   襯ਢ񭭮 㭪樨 C(x). 祭
x,  ஬ ⨣ ,  㤥 ᪮. 
 ᪠  ᫥ ⮤,  ஡ 뢥
 (ࠢ  ந 㭪樨 C(x)  
祭 ࠢ -   ᯮᮡ   ஡).
     . 12 ਢ 䨪 㭪樨 C(x)  k=1,2,3,4,5.
 ⬥祭 묨 窠. ,    k=1, 
  業  ᥫ ࠢ 業 ୮, 룮
 ࠢ  㫥    ४஢ 
(      ४஢).   ⮬ k 
㫥  ४஢  ⠪  , ⮡
C 뫠 쭮.

                      Ŀ
                      12.gif              
                                          
                                          
                                          
                                          
                                          
                      
                             . 12

    祭 x,   ⨣  C, 
ᮮ⢥騥  祭 C ਢ  ⠡. 1.
 ⠬ ਢ 砥 먣  ४஢ - 
᪮쪮 業⮢ 襢 砥  ଠ樨 (.. 
᪮쪮 業⮢ 쭮 C , 祬 C(0,5)).

            ͻ
             k   x     C    砥 먣 
            Ķ
             1  0,50  1,00         0,0%        
            Ķ
             2  0,62  1,44         4,0%        
            Ķ
             3  0,68  1,81         9,3%        
            Ķ
             4  0,72  2,15        14,0%        
            Ķ
             5  0,75  2,46        17,8%        
            ͼ
                            . 1

     . 13   㢨 䨪 ᨬ x  k 
 k  1  10.

                      Ŀ
                      13.gif              
                                          
                                          
                                          
                                          
                                          
                      
                             . 13

    ⠪,  ᬮ ।  ࠪ⨪
쭮 ४஢騪: ।  㫥 
४஢  (  室  ।
ᮮ⭮襭 㫥    ४஢ )  ।
業    室  ᫥ ४஢.
 ࠧ,  ࠧࠡ⪥ ᢮ ४஢騪  稫
 ਥ஢   ࠪ⨪.

      ਢ  ࠧ  ४஢.

    ࢠ : ந 䨪   ᮮ⭮襭 0  1,
  ⥮᪨ ⨬쭮. 室  㤥
஢ 㯯  n ⮢ (祬  n, ⥬ ), 
祣 ந ॢ  2^n ﬨ. ந ॢ ᢥ ,
   ࠧ⢫ 롨ࠥ ᮮ⭮襭  쥢
   ॢ ( 設 0   設 1)
⠪, ⮡  뫮    ⥮᪨ ⨬쭮
ᮮ⭮襭 (, 筮, ⮡ 稫    
   ॢ). ⮬  룮  讥 n -
⮣ ᮮ⭮襭     ⨬.
      ᯮ - ⥫⢮ ⮣, 
祭  ⮬  䨪  㤥 訬 
  䨪    n.
    ⨢ ᭮ ⬠ ᫥饥: ⠪  
ࠧ  ॢ ᮮ⢥    - 㯯
 (⠪, ᠬ  ࠧ ᮮ⢥ ࢮ 
  ),   ᫮    ࠢ,
, 롨 ᮮ⭮襭  쥢  ॢ 
   ⨬쭮,  , ⮡ ᮮ⭮襭
㫥    ⮬   ⮩ 㯯  뫮  
⨬쭮.  ⠪ ,  ᢮ ।,    
ᮮ⢥ - ࠧ ॢ,  ᮮ⭮襭 㫥 
    㤥  । 筮  
⨬쭮:     - ᮡ , 
 ᫥  -  ।    (⭮, 
   讥 楫 ᫮   楫 ᫠  㦭
ய樨, 譮  । 㤥 , 祬  
 襥 ᫮  ⮩  ய樨).  ᫥  
ᠬ   ᮮ⭮襭 㫥   㤥 ᥣ
1:1 - ⮬ ⠪ ஢  쭮.
    த ࠡ ⬠  ਬ.  k=3,
⮣ x~=0,68 (. ⠡. 1),  ⭮襭 ⢠ 㫥
     ࠢ ਬ୮ 2,13.  n=4,
.. 㥬 㯯   .
      - ,  ॢ 㤥 16 쥢. 
    ⠪, ⮡ ⢮ 쥢  ࢮ 
⭮ᨫ   쥢  ன   
 2,13. 砥 11 쥢  ࢮ   5  ன. 
ࠧ,  ॢ  設 0 㤥 11 쥢,  
ॢ  設 1 - 5 쥢. ⠪,  ஢ ॢ
㤥 룫拉 ᫥騬 ࠧ:

                             Ŀ
                           0(11)  1(5)

    ன ஢. 筮 ࠧ 11  7  4,  5 -  3
 2:

                         Ŀ
                      0Ŀ      1Ŀ
                     0(7)  1(4)   0(3)  1(2)

    ⨩ ஢.  7  5  2, 4 -  3  1, 3 -  2
 1, 2 -  1  1:

                     Ŀ
              0Ŀ          1Ŀ
           0Ŀ      1Ŀ    0Ŀ    1Ŀ
          0(5)  1(2)   0(3)   1   0(2)   1    0   1

     ஢.  5  3  2, 2 -  1  1, 3 -
 2  1:

                     Ŀ
           0Ŀ           1Ŀ
     0Ŀ         1Ŀ     0Ŀ    1Ŀ
  0Ŀ      1Ŀ    0Ŀ  1   0Ŀ   1    0   1
 0(3)  1(2)    0   1   0(2)   1      0   1

     ஢.  3  2  1, 2 -  1  1:

                          Ŀ
                0Ŀ          1Ŀ
          0Ŀ         1Ŀ    0Ŀ    1Ŀ
     0Ŀ    1Ŀ    0Ŀ  1  0Ŀ   1    0   1
  0Ŀ    1Ŀ  0   1  0Ŀ   1     0   1
 0(2)   1    0   1         0   1

    ⮩ ஢.  2  1  1:

                          Ŀ
                0Ŀ          1Ŀ
          0Ŀ         1Ŀ    0Ŀ    1Ŀ
     0Ŀ    1Ŀ    0Ŀ  1  0Ŀ   1    0   1
  0Ŀ    1Ŀ  0   1  0Ŀ   1     0   1
0Ŀ   1    0   1         0   1
0   1

    ॢ ஥, ⥯ ந ࠧ (⠪ 
⭮  権  室  )
ᮯ⠢塞 16 権  16 祭묨  - ਬ,
⠪:

    0000 -> 000000
    0001 -> 000001
    0010 -> 00001
    0011 -> 00010
    0100 -> 00011
    0101 -> 0010
    0110 -> 0011
    0111 -> 01000
    1000 -> 01001
    1001 -> 0101
    1010 -> 011
    1011 -> 1000
    1100 -> 1001
    1101 -> 101
    1110 -> 110
    1111 -> 111

    ⢮ 㫥   16  - 44,  - 25.
⭮襭 44/(44+25)~=0,64,  筮  
⥮᪨ ⨬쭮 ~0,68.  ।  ஢
 ⮢   44/16=2,75 㫥  25/16=1,5625
.  業  ⮢ - 2,75+3*1,5625=7,4375 ..
     ࠧ   ਬ୮ ࠢ 1,86 ..
 ᫨    ४஢  - 業 뫠  ࠢ
2 ..

      ४஢ - ᯮ짮 䬥᪮
ᦠ⨥ "". ⭮,  ᫨  室 
ᮮ⭮襭 0  1 ⫨砥  1:1,   ᦠ   
䬥᪮ ⮤.  ᮪,  㫥  
⠭ ਬ୮ ஢.    ⭠ : 
室 ,  㫥   ਬ୮ ஢ (
᫮ ),     襣 ࠧ,  
 ᮮ⭮襭 㫥  .   
室  㯠묨 䬥᪨ ⮤ 
ᯠ , 稢 㦭 ᮮ⭮襭 0  1 ( ࠧ
).  ⥭  - , ᦨ ⠭ ,
  १ 砥 室 .  ⠪ . 
ࠪ⨪  ஢. :-)


筨


1. FIDO-७ RU.ALGORITHMS, ⥬ "⠭
   ࠦ".
   http://groups.google.com.ru/groups?dq=&hl=ru&lr=&ie=UTF-8&inlang=ru&threadm=1043288021%40p5.f1826.n5020.z2.FidoNet.ftn&prev=/groups%3Fdq%3D%26num%3D25%26hl%3Dru%26lr%3D%26ie%3DUTF-8%26inlang%3Dru%26group%3Dfido7.ru.algorithms%26start%3D550

2. "稩 ". "" 14/2001, . 11.
   http://www.computerra.ru/offline/2001/391/8434/page3.html

3. "ਫ   ࠭...". "" 14-15/2003,
   . 10.
   http://www.computerra.ru/offline/2003/489/26108/page2.html

4. .祭. "... ୨  ". ""
   14/2000, . 12.

5. " ᠫ  㣮...". "" 25/2002, . 6.
   http://www.computerra.ru/offline/2002/450/18645/

6. ..楢. "䬥⨪ ஢ 設". ᪢, "㪠",
   1969.
