90 lines
2.6 KiB
Mathematica
90 lines
2.6 KiB
Mathematica
clear all;
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global N
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global R
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global A
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#-------------------------------------------------------------------------------
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function retval = f1(theta)
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global N;
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global R;
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retval=0.0;
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gterm = gammaln(N/2) - gammaln((N+1)/2) - log(2*sqrt(pi));
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rhs = -N*R*log(2);
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lhs=gterm + (N-1)*log(sin(theta)) + log(1-(tan(theta).^2)/N) - log(cos(theta));
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retval = rhs-real(lhs);
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endfunction
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#-------------------------------------------------------------------------------
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#-------------------------------------------------------------------------------
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function retval = d(N,i,x)
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t1=(x.^2)/2;
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t2=gammaln(N/2);
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t3=-gammaln(i/2+1);
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t4=-gammaln(N-i);
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t5=(N-1-i)*log(sqrt(2)*x);
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t6=-log(2)/2;
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t7arg=1+(-1)^i * gammainc((x.^2)/2.0,(i+1)/2);
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t7=log(t7arg);
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retval=t1+t2+t3+t4+t5+t6+t7;
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endfunction
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#-------------------------------------------------------------------------------
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#-------------------------------------------------------------------------------
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function retval = maxstar(x1,x2)
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retval = max(x1,x2)+log(1+exp(-abs(x1-x2)));
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endfunction
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#-------------------------------------------------------------------------------
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#-------------------------------------------------------------------------------
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function retval = spb_integrand(x)
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global N;
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global A;
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t1=log(N-1);
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t2=-N*(A^2)/2;
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t3=-0.5*log(2*pi);
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t4=(N-2)*log(sin(x));
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arg=sqrt(N)*A*cos(x);
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t5=maxstar(d(N,0,arg),d(N,1,arg));
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for i=2:N-1
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t5=maxstar(t5,d(N,i,arg));
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endfor
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retval=exp(t1+t2+t3+t4+t5);
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endfunction
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#-------------------------------------------------------------------------------
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#-------------------------------------------------------------------------------
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function retval = qfunc(x)
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retval = 0.5 * erfc(x/sqrt(2));
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endfunction
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#-------------------------------------------------------------------------------
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#-------------------------------------------------------------------------------
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# Calculate sphere packing lower bound on the probability of word error
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# given block length (N), code rate (R), and Eb/No.
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#
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# Ref:
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# "Log-Domain Calculation of the 1959 Sphere-Packing Bound with Application to
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# M-ary PSK Block Coded Modulation," Igal Sason and Gil Weichman,
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# doi: 10.1109/EEEI.2006.321097
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#-------------------------------------------------------------------------------
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N=174
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K=75
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R=K/N
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delta=0.01;
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[ths,fval,info,output]=fzero(@f1,[delta,pi/2-delta], optimset ("jacobian", "off"));
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for ebnodb=-6:0.5:4
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ebno=10^(ebnodb/10.0);
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esno=ebno*R;
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A=sqrt(2*esno);
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term1=quadcc(@spb_integrand,ths,pi/2);
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term2=qfunc(sqrt(N)*A);
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pe=term1+term2;
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ps=1-pe;
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printf("%f %f\n",ebnodb,ps);
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endfor
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