SVN r8748

2018-06-14 21:27:34 -04:00
parent 419c039d08
commit 4f1fe4fc94
581 changed files with 69338 additions and 39836 deletions
@@ -0,0 +1,89 @@
+clear all;
+global N
+global R
+global A
+
+#-------------------------------------------------------------------------------
+function retval = f1(theta)
+  global N;
+  global R;
+  retval=0.0;
+  gterm = gammaln(N/2) - gammaln((N+1)/2) - log(2*sqrt(pi));
+  rhs = -N*R*log(2);
+  lhs=gterm + (N-1)*log(sin(theta)) + log(1-(tan(theta).^2)/N) - log(cos(theta));
+  retval = rhs-real(lhs);
+endfunction
+#-------------------------------------------------------------------------------
+
+#-------------------------------------------------------------------------------
+function retval = d(N,i,x)
+  t1=(x.^2)/2;
+  t2=gammaln(N/2);
+  t3=-gammaln(i/2+1);
+  t4=-gammaln(N-i);
+  t5=(N-1-i)*log(sqrt(2)*x);
+  t6=-log(2)/2;
+  t7arg=1+(-1)^i * gammainc((x.^2)/2.0,(i+1)/2);
+  t7=log(t7arg);
+  retval=t1+t2+t3+t4+t5+t6+t7;
+endfunction
+#-------------------------------------------------------------------------------
+
+#-------------------------------------------------------------------------------
+function retval = maxstar(x1,x2)
+  retval = max(x1,x2)+log(1+exp(-abs(x1-x2)));
+endfunction
+#-------------------------------------------------------------------------------
+
+#-------------------------------------------------------------------------------
+function retval = spb_integrand(x)
+ global N;
+ global A;
+
+ t1=log(N-1);
+ t2=-N*(A^2)/2;
+ t3=-0.5*log(2*pi);
+ t4=(N-2)*log(sin(x));
+
+ arg=sqrt(N)*A*cos(x);
+ t5=maxstar(d(N,0,arg),d(N,1,arg));
+ for i=2:N-1
+   t5=maxstar(t5,d(N,i,arg));
+ endfor
+
+ retval=exp(t1+t2+t3+t4+t5);
+endfunction
+#-------------------------------------------------------------------------------
+
+#-------------------------------------------------------------------------------
+function retval = qfunc(x)
+  retval = 0.5 * erfc(x/sqrt(2));
+endfunction
+#-------------------------------------------------------------------------------
+
+#-------------------------------------------------------------------------------
+# Calculate sphere packing lower bound on the probability of word error
+# given block length (N), code rate (R), and Eb/No.
+# 
+# Ref: 
+# "Log-Domain Calculation of the 1959 Sphere-Packing Bound with Application to 
+# M-ary PSK Block Coded Modulation," Igal Sason and Gil Weichman, 
+# doi: 10.1109/EEEI.2006.321097
+#-------------------------------------------------------------------------------
+N=174
+K=75
+R=K/N
+
+delta=0.01;
+[ths,fval,info,output]=fzero(@f1,[delta,pi/2-delta], optimset ("jacobian", "off"));
+
+for ebnodb=-6:0.5:4
+  ebno=10^(ebnodb/10.0);
+  esno=ebno*R;
+  A=sqrt(2*esno);
+  term1=quadcc(@spb_integrand,ths,pi/2);
+  term2=qfunc(sqrt(N)*A);
+  pe=term1+term2;
+  ps=1-pe;
+  printf("%f %f\n",ebnodb,ps);
+endfor
@@ -1,67 +0,0 @@
-<HTML><HEAD>
-
-<TITLE> Github Facilities </TITLE>
-
-</HEAD><BODY>
-
-<H1> Github Facilities </H1>
-
-<P>Starting with the Version of 2012-02-11, the source code repository
-for this software is hosted by <A HREF="http://github.com">Github</A>,
-and is located at <A
-HREF="http://github.com/radfordneal/LDPC-codes">http://github.com/radfordneal/LDPC-codes</A>.
-This repository includes the annotated log of changes made since the
-Version of 2006-02-08.
-
-<P>You can use the facilities at Github to obtain the source-code
-repository, report bugs, and contribute to the wiki.
-
-<H2>Obtaining the source repository, and modifying it</H2>
-
-<P>To obtain a copy of the source-code repository, issue the following
-command (in a Unix/Linux/Cygwin environment that has git installed):
-<BLOCKQUOTE><PRE>
-git clone git://github.com/radfordneal/LDPC-codes
-</PRE></BLOCKQUOTE>
-This will retrieve the current state of the software, storing it
-in the directory <TT>LDPC-codes</TT>, which you should ensure does not
-exist before issuing this command above.
-
-<P>Note that if all you want to do is compile and use the current
-version, you can instead download the source without development
-history as described in the <A HREF="install.html">installation 
-instructions</A>. 
-
-<P>The <TT>LDPC-codes</TT> directory created by the <TT>git clone</TT>
-command is a git repository, which can be manipulated with the various
-forms of the <TT>git</TT> command, which are documented, for example,
-<A HREF="http://git-scm.com/documentation">here</A>.  
-
-<P>Each stable version of the software is a separate branch of the
-repository.  The documentation on the most recent stable version is in
-the "gh-pages" branch. The current development version is on the
-"master" branch.  The are other branches for each stable version that
-was released.
-
-<P>You can make local changes to your copy of the repository, and use
-the modified software.  If you wish, you can ask me
-(radfordneal@gmail.com) to include your changes in a new release, or,
-if you register as a <A HREF="http://github.com">Github</A> user, you can set
-up your own fork of the software for you and other people to use.
-
-
-<H2>Reporting Bugs</H2>
-
-You can use the Github "Issues" facility to report bugs in the
-software.  You have to register as a <A HREF="github.com">Github</A>
-user to do this (which is free).  You can then go <A
-HREF="https://github.com/radfordneal/LDPC-codes/issues">here</A> and
-click on "New issue" to report a bug.  You can also use this facility
-to suggest new features or other revisions. I may not have time to
-implement them, but perhaps someone else will.
-
-<HR>
-
-<A HREF="index.html">Back to index for LDPC software</A>
-
-</BODY></HTML>