%?function?[degreesrholambdastats]=CompLeftExp（Ra）;
%
%?Computes?degree?distributions?from?the?exponential
%?family
%
%??f（x;a）?=（exp（a*x）-1）/（exp（a）-1）
%
%?（“Tornado?sequences“）.?Uses?explicit?formulas?for?the?Taylor
%?coefficients?of?f?and?g.
%
%?Input:?Rate?00
%?
%?Output:
%??degrees=[a_r?a_l?N?M]?average?and?maximal?degrees?
%??????????of?right?and?left?degree?distributions
%??rho?????1xN?array?of?right?degrees
%??lambda??1xM?array?of?left?degrees
%??stats???[deltaepsilonmuDeltaLambda2]??
%??????????distances?to?capacity?1-R?comparison?to
%??????????lower?bounds?and?fraction?of?degree?2?variable
%??????????nodes??Lambda2=lambda2*a_l/2
%
%?Author:?P.?Oswald
%?Last?changed:?10/4/2002

function?[degreesrholambdastats]=CompLeftExp（Ra）;
%
%?Safety?bounds?for?degrees
Nmax=20000;Mmax=20000;
%?Computation?of?a_r?N?and?rho
%?by?taking?a?long?enough?piece?of?the?Taylor?series?of?f
b=exp（a）-1;Ir0=（b-a）/（a*b）;?%?Ir0?=?int_[01]?f（x）?dx
rho=[];c=a/b;Ir=0;n=2;
while?Ir0-Ir>0.0000000001&n<=Nmax
??rho=[rho?c];c=c/n;Ir=Ir+c;c=c*a;n=n+1;?
?end
c1=sum（rho）;rho=rho/c1;N=n-1;ar=c1/Ir;
%
%?Computation?of?a_l?M?lambda?and?delta?
%?by?implementing?Step?（2）?and?（3）?of?Algorithm?1.
%?This?is?based?on?hand-derived?recursions?for?the?Taylor?coefficients
%?g_k?of?g?which?lead?to?recursions?for?s_k?and?sigma_k?and?finally
%?to?finding?t?such?that?hat（I）（t）=1/a_l?where?a_l=a_r*（1-R）
%?is?the?average?degree?of?the?left?（variable）?nodes.
al=ar*（1-R）;b=b/exp（a）;
c=b/a;sk=c;c1=c/2;sigmak=c1;lambda=[];
if?al<2
??disp（‘Average?degree?of?left?nodes?too?small?（decrease?R?or?increase?a）‘）;
??M=0;lambda=[];stats=[];
?else
??if?al==2
????lambda=1;M=2;delta=c;
???else
????m=2;q=sigmak/sk;
????while?q*al>1&m??????lambda=[lambda?c];c=c1*b*（m-1）;sk=sk+c;
??????m=m+1;c1=c/m;sigmak=sigmak+c1;q0=q;q=sigmak/sk;
?????end
????if?q*al>1&m==Mmax
??????disp（‘M?too?big?（reduce?a?or?increase?R?or?change?Mmax）‘）;
??????M=m;lambda=[];stats=[];
?????else
??????M=m;t1=（al*sigmak-sk）/（al*c1-c）;
??????delta=（sk-t1*c）;lambda=[lambda?（1-t1）*c]/delta;
?????end
???end
??%
??%?Computation?of?output
??epsilon=1-delta/（1-R）;
??b=ar*log（R）;mu=b/log（epsilon）;Delta=epsilon/exp（b）;
??Lambda2=lambda（1）*al/2;stats=[delta?epsilon?mu?Delta?Lambda2];
?end
degrees=[ar?al?N?M];
%?End?CompLeftExp.m

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2011-05-16?13:32??chandhuLDPC\
?????文件????????2383??2009-01-05?21:02??chandhuLDPC\CompLeftExp.m
?????文件????????2154??2011-05-12?18:32??chandhuLDPC\CompLeftPoly.m
?????文件????????2273??2009-01-05?21:03??chandhuLDPC\CompLeftPoly2c.m
?????文件????????2782??2009-01-05?21:05??chandhuLDPC\CompLeftSelf.m
?????文件????????1570??2009-01-05?21:08??chandhuLDPC\main.m