MATLAB Examples

Rate 2/3 Convolutional Code in AWGN

This example generates a bit error rate versus Eb/No 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 = 16;
codeRate = 2/3;

Create a convolutional encoder and its equivalent Viterbi decoder.

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

Create a 16-QAM modulator and demodulator pair having bit inputs and outputs. Set the constellation to normalize on average power.

qamModulator = comm.RectangularQAMModulator('BitInput',true,'NormalizationMethod','Average power');
qamDemodulator = comm.RectangularQAMDemodulator('BitOutput',true,'NormalizationMethod','Average power');

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/No values to be simulated. Initialize the bit error rate statistics matrix.

ebnoVec = 0:2:10;
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.
  • Modulate the encoded data.
  • Pass the signal through an AWGN channel.
  • Demodulate the received signal.
  • Decode the demodulated signal by using a Viterbi decoder.
  • Collect the error statistics.
for m = 1:length(ebnoVec)
    snr = ebnoVec(m) + 10*log10(k*codeRate);
    while errorStats(m,2) <= 100 && errorStats(m,3) <= 1e7
        dataIn = randi([0 1],10000,1);
        dataEnc = convEncoder(dataIn);
        txSig = qamModulator(dataEnc);
        rxSig = awgn(txSig,snr);
        demodSig = qamDemodulator(rxSig);
        dataOut = vitDecoder(demodSig);
        errorStats(m,:) = errorRate(dataIn,dataOut);

Compute the theoretical BER vs. Eb/No curve for the case without forward error correction coding.

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

Plot the BER vs. Eb/No curve for the simulated coded data and the theoretical uncoded data.

semilogy(ebnoVec,[errorStats(:,1) berUncoded])
xlabel('Eb/No (dB)')
ylabel('Bit Error Rate')

At higher Eb/No values, the error correcting code provides performance benefits.