MATLAB, 1960 bps
Here is my updated attempt:
fs = 44100; %44.1kHz audio rate
fc = 2450; %2.45kHz carrier - nice fraction of fs!
fsym = fc/5; %symbol rate
tmax = 4; %about 4 seconds worth
preamblesyms = 6;
t = 1/fs:1/fs:(tmax+preamblesyms/fsym);
symbols = preamblesyms+fsym*tmax;
symbollength = length(t)/symbols;
bits = symbols*3;
bitstream = [zeros(1,preamblesyms*3),rand(1,bits-preamblesyms*3)>0.5]; %Add a little preamble of 18 bits
data = bin2dec(char(reshape(bitstream,3,symbols)'+'0'))';
greycode = [0 1 3 2 6 7 5 4];
%Encode the symbols using QAM8 - we use effectively grey code so that
%adjacent symbols in the constellation have only one bit difference
%(minimises error rate)
encoded = zeros(2,symbols);
encoded(1,data==1) = 1/sqrt(2);
encoded(1,data==3) = 1;
encoded(1,data==2) = 1/sqrt(2);
encoded(1,data==7) = -1/sqrt(2);
encoded(1,data==5) = -1;
encoded(1,data==4) = -1/sqrt(2);
encoded(2,data==0) = 1;
encoded(2,data==1) = 1/sqrt(2);
encoded(2,data==2) = -1/sqrt(2);
encoded(2,data==6) = -1;
encoded(2,data==7) = -1/sqrt(2);
encoded(2,data==4) = 1/sqrt(2);
%Modulate onto carrier
carrier = [sin(2*pi*fc*t);cos(2*pi*fc*t)];
signal = reshape(repmat(encoded(1,:)',1,symbollength)',1,[]);
signal(2,:) = reshape(repmat(encoded(2,:)',1,symbollength)',1,[]);
modulated = sum(signal.*carrier)';
%Write out an audio file
audiowrite('audio.wav',modulated,fs);
%Wait for the user to run through the POTS simulator
input('');
%Read in the filtered data
filtered=audioread('audio.pots-filtered.wav')';
%Recover the two carrier signals
preamblecos = filtered(symbollength+1:symbollength*2);
preamblesin = filtered(symbollength+1+round(symbollength*3/4):symbollength*2+round(symbollength*3/4));
%Replicated the recovered carriers for all symbols
carrierfiltered = [repmat(preamblesin,1,symbols);repmat(preamblecos,1,symbols)];
%Generate a demodulation filter (pass up to 0.66*fc, stop at 1.33*fc
%(really we just need to kill everything around 2*fc where the alias ends up)
d=fdesign.lowpass('Fp,Fst,Ap,Ast',0.05,0.1,0.5,60);
Hd = design(d,'equiripple');
%Demodulate the incoming stream
demodulated = carrierfiltered .* [filtered;filtered];
demodulated(1,:)=filtfilt(Hd.Numerator,1,demodulated(1,:));
demodulated(2,:)=filtfilt(Hd.Numerator,1,demodulated(2,:));
%Split signal up into bit periods
recovereddemodulated=[];
recovereddemodulated(1,:,:) = reshape(demodulated(1,:),symbollength,symbols);
recovereddemodulated(2,:,:) = reshape(demodulated(2,:),symbollength,symbols);
%Extract the average level for each bit period. Only look at the second
%half to account for slow rise times in the signal due to filtering
recoveredsignal=mean(recovereddemodulated(1,round(symbollength/2):symbollength,:));
recoveredsignal(2,:)=mean(recovereddemodulated(2,round(symbollength/2):symbollength,:));
%Convert the recovered signal into a complex number.
recoveredsignal=recoveredsignal(2,:) + 1j*recoveredsignal(1,:);
%Determine the magnitude and angle of the symbol. The phase is normalised
%to pi/4 as that is the angle between the symbols. Rounding this to the
%nearest integer will tell us which of the 8 phases it is closest to
recoveredphase = round(angle(recoveredsignal)/(pi/4));
recoveredphase = mod(recoveredphase+8,8)+1; %Remap to an index in the grey code vector.
%Determine the symbol in the QAM8 constellation
recoveredencoded=greycode(recoveredphase);
recoveredencoded(1:preamblesyms)=0; %Assume the preamble is correct for comparison
%Turn it back in to a bit stream
bitstreamRecovered = reshape(dec2bin(recoveredencoded)'-'0',1,[]);
%And check if they are all correct...
if(all(bitstream==bitstreamRecovered))
disp(['Woop, ' num2str(fsym*4) 'bps']);
else
error('Its corrupt Jim.');
end
Since my first attempt, I have played around a bit. There is now a small preamble at the beginning (18 bit periods, but could be shorter) which contains just a cosine wave. I extract this and replicated it to create correctly phased sine and cosine carriers for demodulation - as it is a very short preamble, I haven't counted it in the bit rate as per your instructions.
Also since the first attempt I am now using a QAM8 constellation to achieve 3 bits per symbol instead of 2. This effectively doubles the transfer rate. So with a ~2.4kHz carrier I am now achieving 1960bps.
I've also improved the symbol detection so that the averaging doesn't get affected by slow rise times caused by the filtering - basically only the second half of each bit period is averaged to remove the impact of rise times.
Still nowhere near the 40kbps theoretical channel bandwidth from the Shannon-Hartley theory (assuming the 30dB SNR)
Just for those that like horrible sounds, this is the new entry:
And in case anyone is interested, this is the previous 960bps entry
2Is this different than an ordinary "compress this binary data" challenge? If so, could you clarify how precisely it differs? – Doorknob – 2015-10-01T01:32:51.867
1Here you're modulating data (turning it into something analog) then the reverse. One could maybe call it "analog compression" – Nick T – 2015-10-01T01:37:25.387
Sorry, I'm not sure I understand how this challenge works. The word "modulate" doesn't even appear in the Wikipedia article you linked. Could you include more background information, or clarify the spec? – Doorknob – 2015-10-01T01:38:56.080
4
wget wikipedia.org/Special:Random | grep title | texttospeech audio.wav
speechtotext POTSaudio.wav | wget wikipedia/wiki/$text
– TessellatingHeckler – 2015-10-01T02:53:54.5901This is an awesome challenge, I will try to find the time to submit an answer! – GoatInTheMachine – 2015-10-01T12:57:35.513