[Octave-bug-tracker] [bug #41407] Implementation of qfunc in comm package

[Tony Richardson]

URL:
  <http://savannah.gnu.org/bugs/?41407>

                 Summary: Implementation of qfunc in comm package
                 Project: GNU Octave
            Submitted by: amrichardson
            Submitted on: Thu 30 Jan 2014 06:25:12 PM GMT
                Category: Octave Forge Package
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Matlab Compatibility
                  Status: None
             Assigned to: None
         Originator Name: Tony Richardson
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.6.4
        Operating System: Any

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Details:

Is it possible to replace the current definition of qfunc in the
communications package with this one?

function y = qfunc2(x)
        y = erfc(x/sqrt(2))/2;
end

The current implementation returns 0 for arguments greater than about 8.  (It
implements qfunc as 1 - normcdf(x) and so relies on the differences between
two numbers that are both about 1.)  The implementation above relies on erfc
and is good down to machine precision. It doesn't return 0 until the argument
is greater than about 38.  The following script illustrates the differences:

k = 0:0.01:20;
figure(1)
subplot(2,1,1)
semilogy(k, qfunc2(k));
ax = axis();
subplot(2,1,2)
semilogy(k, qfunc(k));
axis(ax);

qfuncinv suffers from similar problems, but unfortunately the fix is not so
simple.  Octave's implementation of erfcinv returns Inf for arguments smaller
than about 1e-17.  MATLAB's implementation doesn't return Inf until the
argument is less than 1e-320 or so.  (I know that such small probabilities are
uncommon in "regular"
statistics, but not uncommon in digital communications where we may be
interested in the probability of one bit error in a
billion/trillion/gazillion.)

Tony Richardson





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