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Rate 2/3 Convolutional Code in AWGN

This example generates a bit error rate versus Eb/N0 curve for a link that uses 16-QAM modulation and a rate 2/3 convolutional code in AWGN.

Set the modulation order, and compute the number of bits per symbol.

M = 16;
k = log2(M);

Create a trellis for a rate 2/3 convolutional code. Set the traceback and code rate parameters.

trellis = poly2trellis([5 4],[23 35 0; 0 5 13]);
traceBack = 28;
codeRate = 2/3;

Create a convolutional encoder and its equivalent Viterbi decoder to run in the continuous mode.

convEncoder = comm.ConvolutionalEncoder(TrellisStructure=trellis);
vitDecoder = comm.ViterbiDecoder( ...
    TrellisStructure=trellis, ...
    InputFormat='Hard', ...

Create an error rate object. Set the receiver delay to twice the traceback depth, which is the delay through the decoder.

errorRate = comm.ErrorRate(ReceiveDelay=2*traceBack);

Set the range of Eb/N0 values to be simulated and compute the equivalent SNR values. Initialize the bit error rate statistics matrix.

ebnoVec = 0:2:10;
snr = convertSNR(ebnoVec,"ebno","snr", ...
    BitsPerSymbol=k, ...
errorStats = zeros(length(ebnoVec),3);

Simulate the link by following these steps:

  • Generate binary data.

  • Encode the data with a rate 2/3 convolutional code.

  • 16-QAM modulate the encoded data, configure bit inputs and unit average power.

  • Pass the signal through an AWGN channel.

  • 16-QAM demodulate the received signal configure bit outputs and unit average power.

  • Decode the demodulated signal by using a Viterbi decoder.

  • Collect the error statistics.

for ii = 1:length(ebnoVec)
    while errorStats(ii,2) <= 100 && errorStats(ii,3) <= 1e7
        dataIn = randi([0 1],10000,1);
        dataEnc = convEncoder(dataIn);
        txSig = qammod(dataEnc,M, ...
        rxSig = awgn(txSig,snr(ii),'measured');
        demodSig = qamdemod(rxSig,M, ...
        dataOut = vitDecoder(demodSig);
        errorStats(ii,:) = errorRate(dataIn,dataOut);

Compute the theoretical BER curve for the case without forward error correction coding by using the berawgn function.

berUncoded_emp = berawgn(ebnoVec','qam',M);

Compute the theoretical BER curve for the case with forward error correction coding by using the bercoding function and the distance spectrum for the 2/3 rate convolutional code. The distspec function computes the distance spectrum of convolutional codes and outputs the distance spectrum structure.

spect = distspec(trellis,4)
spect = struct with fields:
     dfree: 5
    weight: [1 6 28 142]
     event: [1 2 8 25]

berCoded_emp = bercoding(ebnoVec', ...

Plot BER versus Eb/N0 curves for the simulated coded data, and the theoretical uncoded and coded data. At higher Eb/N0 values, the error correcting code provides performance benefits. The simulated coded error rate results show good correlation to the theoretical coded results.

semilogy(ebnoVec,errorStats(:,1),'b*', ...
    ebnoVec,berUncoded_emp,'c-', ...
legend('Coded simulated','Uncoded theoretical','Coded theoretical', ...
title('16-QAM With and Without Forward Error Correction')
xlabel('Eb/N0 (dB)')
ylabel('Bit Error Rate')

Figure contains an axes object. The axes object with title 16-QAM With and Without Forward Error Correction, xlabel Eb/N0 (dB), ylabel Bit Error Rate contains 3 objects of type line. One or more of the lines displays its values using only markers These objects represent Coded simulated, Uncoded theoretical, Coded theoretical.