diff --git a/lib/fsk4hf/spb.m b/lib/fsk4hf/spb.m new file mode 100644 index 000000000..cc8103aac --- /dev/null +++ b/lib/fsk4hf/spb.m @@ -0,0 +1,84 @@ +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. +#------------------------------------------------------------------------------- +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