The X we used is what we call the âX-factorâ. An X- factor of zero means all the symbols in the table have the same probability, which means the Huffman coding ...
/2:32:(5/22.837$%/(6)25+8))0$1'(&2',1* -DVRQ0F1HHO\DQG0DJG\%D\RXPL ^MEPPDE`#FDFVORXLVLDQDHGX 7KH&HQWHUIRU$GYDQFHG&RPSXWHU6WXGLHV 8QLYHUVLW\RI/RXLVLDQDDW/DID\HWWH
$%675$&7
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²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
1-4244-1437-7/07/$20.00 ©2007 IEEE
%LW6WUHDP &E
9/&'HWHFWRU &D
FRQWURO
O
/87 6
'HFRGHG6\PEROV )LJXUH 7\SLFDO9/&GHFRGHU
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µ$¶ µ%¶ µ&¶DQGµ'¶DVSRVVLEOHV\PEROV/HWWKHLUFRGHZRUGVEH DQGUHVSHFWLYHO\/HWWKHLQFRPLQJELWVWUHDPEH ZKLFKLVµ$¶µ'¶µ$¶ &EZRXOGILUVWEHVHWWR DQGORDGHGLQWRWKH9/&'HWHFWRU7KLVLVEHFDXVHWKH9/& GHWHFWRUPXVWEHDEOHWRKDQGOHWKHODUJHVWFRGHZRUGZKLFK LQWKLVFDVHLVELWV6LQFHWKHDFFXPXODWRU FRQWUROOHU VWDUWV
VI - 465
ICIP 2007
DWQRVKLIWLQJRFFXUVVR&DDOVREHFRPHV7KH/87 GHFRGHV WKH LQ WKH 06% RI &D DV µ$¶ ZKLFK LV VHQW RXW WKURXJK 6 7KH /87 DOVR VHWV O WR RQH LQGLFDWLQJ WR WKH DFFXPXODWRUFRQWUROOHU WKDW WKH 9/& GHWHFWRU QHHGV WR VKLIW RQFH6R&DWKHQEHFRPHV; DOOELWVVKLIWHGOHIWE\RQH 7KHµ;¶LVDFWXDOO\Dµ¶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¶VWRWKHRU EDQNV6RIURPWKHSUHYLRXVH[DPSOHLI&D WKHILUVW GHPX[ZRXOGSURSDJDWHWKH RUWRNHQ WROHDIµ$¶ZKLFKLV DFWLYDWHG DQG VHQGV RXW WKH V\PERO $ ZKLFK PD\ EH UHSUHVHQWHG E\ RQ OLQH 6 DQG WKH OHQJWK RI WR WKH RU EDQNV 7KH RWKHU OHDYHV GLG QRW JHW WKH WRNHQ VLQFH LW ZHQW RQO\GRZQRQHEUDQFKRIWKHWUHH$OORWKHUOHDYHV VWRUDJH FHOOV WKHUHIRUHFRQWLQXHRXWSXWWLQJ]HURWRWKHRUEDQNV
)LJXUH 7UHH6WUXFWXUH/87
7KH WUHH KDV QRW UHFHLYHG PXFK DWWHQWLRQ LQ UHVHDUFK OLWHUDWXUH ODWHO\ SUREDEO\ GXH WR LWV ORZHU VSHHG ZKLFK FRQWUDGLFWVWKHKLJKVSHHGJRDOVRIPRVWGHVLJQV+RZHYHU ZHZLOOVKRZLWKDVSRZHUDGYDQWDJHVDQGWKXVFDQEHXVHG DVDORZSRZHUORRNXSWDEOHLQVRPHFDVHV 7(670(7+2'2/2*@ $GYDQFHGYLGHRFRGLQJIRUJHQHULFDXGLRYLVXDOVHUYLFHV,78 7UHFRPPHQGDWLRQ+0D\ >@ '$+XIIPDQ³$PHWKRGIRUWKHFRQVWUXFWLRQRIPLQLPXP UHGXQGDQF\FRGHV´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
