Rate 2/3 Convolutional Code in AWGN

This example generates a bit error rate versus ${\mathit{E}}_{\mathit{b}}/{\mathit{N}}_0$ 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', ...
    TracebackDepth=traceBack);

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 ${\mathit{E}}_{\mathit{b}}/{\mathit{N}}_0$ 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, ...
    CodingRate=codeRate);
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, ...
            InputType='bit',UnitAveragePower=true);
        rxSig = awgn(txSig,snr(ii),'measured');
        demodSig = qamdemod(rxSig,M, ...
            OutputType='bit',UnitAveragePower=true);
        dataOut = vitDecoder(demodSig);
        errorStats(ii,:) = errorRate(dataIn,dataOut);
    end
    reset(errorRate)
end

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', ...
    'conv','hard',codeRate,spect,'qam',M);

Plot BER versus ${\mathit{E}}_{\mathit{b}}/{\mathit{N}}_0$ curves for the simulated coded data, and the theoretical uncoded and coded data. At higher ${\mathit{E}}_{\mathit{b}}/{\mathit{N}}_0$ 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-', ...
    ebnoVec,berCoded_emp,'r')
grid
legend('Coded simulated','Uncoded theoretical','Coded theoretical', ...
     'Location','southwest')
title('16-QAM With and Without Forward Error Correction')
xlabel('Eb/N0 (dB)')
ylabel('Bit Error Rate')