ch11.12.htm
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<TD><P CLASS="Table"><A NAME="pgfId=165707"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165709"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165711"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165713"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165715"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165717"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165719"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165721"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165723"></A>01</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165725"></A>S<SUB CLASS="Subscript">2</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165727"></A>S<SUB CLASS="Subscript">1</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165729"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165731"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165733"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165735"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165737"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165739"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165741"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165743"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165745"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165747"></A>11</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165749"></A>S<SUB CLASS="Subscript">3</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165751"></A>S<SUB CLASS="Subscript">2</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165753"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165755"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165757"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165759"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165761"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165763"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165765"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165767"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165769"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165771"></A>00</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165773"></A>S<SUB CLASS="Subscript">0</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165775"></A>S<SUB CLASS="Subscript">2</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165777"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165779"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165781"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165783"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165785"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165787"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165789"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165791"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165793"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165795"></A>10</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165797"></A>S<SUB CLASS="Subscript">1</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165799"></A>S<SUB CLASS="Subscript">2</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165801"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165803"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165805"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165807"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165809"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165811"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165813"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165815"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165817"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165819"></A>00</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165821"></A>S<SUB CLASS="Subscript">0</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165823"></A>S<SUB CLASS="Subscript">2</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165825"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165827"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165829"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165831"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165833"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165835"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165837"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165839"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165841"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165843"></A>10</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165845"></A>S<SUB CLASS="Subscript">1</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165847"></A>S<SUB CLASS="Subscript">3</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165849"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165851"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165853"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165855"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165857"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165859"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165861"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165863"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165865"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165867"></A>01</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165869"></A>S<SUB CLASS="Subscript">2</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165871"></A>S<SUB CLASS="Subscript">3</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165873"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165875"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165877"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165879"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165881"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165883"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165885"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165887"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165889"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165891"></A>11</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165893"></A>S<SUB CLASS="Subscript">3</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165895"></A>S<SUB CLASS="Subscript">3</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165897"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165899"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165901"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165903"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165905"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165907"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165909"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165911"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165913"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165915"></A>01</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165917"></A>S<SUB CLASS="Subscript">2</SUB></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=165919"></A>S<SUB CLASS="Subscript">3</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=165921"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165923"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165925"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165927"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=165929"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165931"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165933"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165935"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165937"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165939"></A>11</TD>
<TD><P CLASS="Table"><A NAME="pgfId=165941"></A>S<SUB CLASS="Subscript">3</SUB></TD></TR>
</TABLE>
<P CLASS="Body"><A NAME="pgfId=133136"></A>As an example, the repeated encoder
input sequence X<SUB CLASS="Subscript">n</SUB> = 0, 1, 2, 3, ... produces
the encoder output sequence Y<SUB CLASS="Subscript">n</SUB> = 1, 0, 5, 4,
... repeated. Table 11.7 shows the state transitions for this sequence,
including the initialization steps.</P>
<P><TABLE BORDER="1" CELLSPACING="2" CELLPADDING="2">
<TR>
<TD><P CLASS="TableFigTitleSide"><A NAME="pgfId=184205"></A>FIGURE 11.4 The
signal constellation for an 8 PSK (phase-shift keyed) code.</TD>
<TD><P><P CLASS="TableFigure"><A NAME="pgfId=184211"></A> </P>
<P><IMG SRC="CH11-42.gif" WIDTH="165" HEIGHT="116" NATURALSIZEFLAG="3" ALIGN="BOTTOM"></TD></TR>
</TABLE>
<TABLE BORDER="1" CELLSPACING="2" CELLPADDING="2">
<TR>
<TD COLSPAN="13"><P CLASS="TableTitle"><A NAME="pgfId=183528"></A>TABLE 11.7 A
sequence of transmitted signals for the rate 2/3 Viterbi encoder</TD></TR>
<TR>
<TD ROWSPAN="2"><P><P CLASS="TableFirst"><A NAME="pgfId=183554"></A>Time</P>
<P><P CLASS="TableFirst"><A NAME="pgfId=183938"></A>ns</TD>
<TD COLSPAN="2"><P CLASS="TableFirst"><A NAME="pgfId=183556"></A><B>Inputs</B></TD>
<TD><P CLASS="Table"><A NAME="pgfId=183560"></A> </TD>
<TD COLSPAN="2"><P CLASS="TableFirst"><A NAME="pgfId=183562"></A>State variables</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183566"></A> </TD>
<TD COLSPAN="3"><P CLASS="TableFirst"><A NAME="pgfId=183568"></A>Outputs</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183574"></A> </TD>
<TD ROWSPAN="2"><P CLASS="TableFirst"><A NAME="pgfId=183576"></A><B>Present state</B></TD>
<TD ROWSPAN="2"><P CLASS="TableFirst"><A NAME="pgfId=183578"></A><B>Next state</B></TD></TR>
<TR>
<TD><P CLASS="Table"><A NAME="pgfId=183585"></A>X<SUB CLASS="Subscript">n</SUB><SUP>2</SUP>
</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183590"></A>X<SUB CLASS="Subscript">n</SUB><SUP>1</SUP>
</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183592"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183597"></A>X<SUB CLASS="Subscript">n-1</SUB><SUP>1</SUP> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183602"></A>X<SUB CLASS="Subscript">n-2</SUB><SUP>1</SUP>
</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183604"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183609"></A>Y<SUB CLASS="Subscript">n</SUB><SUP>2</SUP>
</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183614"></A>Y<SUB CLASS="Subscript">n</SUB><SUP>1</SUP>
</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183619"></A>Y<SUB CLASS="Subscript">n</SUB><SUP>0</SUP>
</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183621"></A> </TD></TR>
<TR>
<TD><P CLASS="TableLeft"><A NAME="pgfId=183627"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183629"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183631"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183633"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183635"></A>x</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183637"></A>x</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183639"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183641"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183643"></A>x</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183645"></A>x</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183647"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183649"></A>S<SUB CLASS="Subscript">?</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=183651"></A>S<SUB CLASS="Subscript">?</SUB></TD></TR>
<TR>
<TD><P CLASS="TableLeft"><A NAME="pgfId=183653"></A>10</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183655"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183657"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183659"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183661"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183663"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183665"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183667"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183669"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183671"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183673"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183675"></A>S<SUB CLASS="Subscript">0</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=183677"></A>S<SUB CLASS="Subscript">1</SUB></TD></TR>
<TR>
<TD><P CLASS="TableLeft"><A NAME="pgfId=183679"></A>50</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183681"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183683"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183685"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183687"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183689"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183691"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183693"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183695"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183697"></A>1</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183699"></A> </TD>
<TD><P CLASS="Table"><A NAME="pgfId=183701"></A>S<SUB CLASS="Subscript">1</SUB></TD>
<TD><P CLASS="Table"><A NAME="pgfId=183703"></A>S<SUB CLASS="Subscript">2</SUB></TD></TR>
<TR>
<TD><P CLASS="TableLeft"><A NAME="pgfId=183705"></A>150</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183707"></A>0</TD>
<TD><P CLASS="Table"><A NAME="pgfId=183709"></A>1</TD>
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