This example shows the application of low density parity check (LDPC) codes in the second generation Digital Video Broadcasting standard (DVB-S.2), which is deployed by DIRECTV in the United States. The example uses communications System objects to simulate a transmitter-receiver chain that includes LDPC encoding and decoding.

The ETSI (European Telecommunications Standards Institute) EN 302 307 standard for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications (DVB-S.2) [ 1 ] uses a state-of-the-art coding scheme to increase the channel capacity. The concatenation of LDPC (Low-Density Parity-Check) and BCH codes is the basis of this coding scheme. LDPC codes, invented by Gallager in his seminal doctoral thesis in 1960, can achieve extremely low error rates near channel capacity by using a low-complexity iterative decoding algorithm [ 2 ]. The outer BCH codes are used to correct sporadic errors made by the LDPC decoder.

The channel codes for DVB-S.2 provide a significant capacity gain over DVB-S under the same transmission conditions. Depending on the transmission mode, DVB-S.2 provides Quasi-Error-Free operation (packet error rate below 10^ -7) at about 0.7 dB to 1 dB from the Shannon limit.

This example simulates the BCH encoder, LDPC encoder, interleaver, modulator, as well as their counterparts in the receiver, according to the DVB-S.2 standard. The example collects the error rate at the demodulator, LDPC decoder, and BCH decoder outputs, determines the distribution of the number of iterations performed by the LDPC decoder, and shows the received symbol constellation. For more information regarding system structure, simplifications, and assumptions, see the DVB-S.2 Link, Including LDPC Coding example for Simulink®.

The configureDVBS2Demo.m script initializes some simulation parameters and generates a structure, dvb. The fields of this structure are the parameters of the DVB-S.2 system at hand. It also creates the System objects making up the DVB-S.2 system.

subsystemType = 'QPSK 1/2'; % Constellation and LDPC code rate EsNodB = 1; % Energy per symbol to noise PSD ratio in dB numFrames = 20; % Number of frames to simulate % Initialize configureDVBS2Demo % Display system parameters dvb

dvb = struct with fields: EsNodB: 1 ModulationType: 'QPSK' NumBytesPerPacket: 188 NumBitsPerPacket: 1504 BCHCodewordLength: 32400 BCHMessageLength: 32208 BCHGeneratorPoly: [1×193 double] BCHPrimitivePoly: [1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1] NumPacketsPerBBFrame: 21 NumInfoBitsPerCodeword: 31584 BitPeriod: 3.1662e-05 LDPCCodewordLength: 64800 LDPCParityCheckMatrix: [32400×64800 logical] LDPCNumIterations: 50 InterleaveOrder: [64800×1 double] Constellation: [4×1 double] SymbolMapping: [0 2 3 1] PhaseOffset: 0.7854 BitsPerSymbol: 2 SequenceIndex: 2 NumSymsPerCodeword: 32400 NoiseVar: 0.7943 NoiseVarEst: 0.5617 RecDelayPreBCH: 32208

The following is a list of objects this example uses:

**Simulation objects:**

enc - BCH encoder dec - BCH decoder LDPCEnc - LDPC encoder LDPCDec - LDPC decoder intrlvr - Block interleaver deintrlvr - Block deinterleaver pskModulator - PSK modulator pskDemodulator - PSK demodulator chan - AWGN channel

**Performance measurement objects:**

PER - Packet error rate calculator BERLDPC - LDPC decoder output error rate calculator BERMod - Demodulator output error rate calculator constDiag - Scatter plot of channel output varCalc - Variance of the noise on a frame meanCalc - Average of the noise variance

Create LDPC encoder and decoder System objects and set the parity check matrix according to Section 5.3.1 of the DVB-S.2 standard [ 1 ]. You set the IterationTerminationCondition property to 'Parity check satisfied' to stop the decoder iterations when all the parity checks are satisfied, which reduces the decoding time. Set the MaximumIterationCount property to 50, to limit the number of simulation iterations. Set the NumIterationsOutputPort to true to output the number of iterations performed for each codeword.

encldpc = comm.LDPCEncoder(dvb.LDPCParityCheckMatrix); decldpc = comm.LDPCDecoder(dvb.LDPCParityCheckMatrix, ... 'IterationTerminationCondition', 'Parity check satisfied', ... 'MaximumIterationCount', dvb.LDPCNumIterations, ... 'NumIterationsOutputPort', true);

This section of the code calls the processing loop for a DVB-S.2 system. The main loop processes the data frame-by-frame, where the system parameter dvb.NumPacketsPerBBFrame determines the number of data packets per BB frame. The first part of the for-loop simulates the system. The simulator encodes each frame using BCH and LDPC encoders as inner and outer codes, respectively. The encoded bits pass through an interleaver. The modulator maps the interleaved bits to symbols from the predefined constellation. The modulated symbols pass through an AWGN channel. The demodulator employs an approximate log-likelihood algorithm to obtain soft bit estimates. The LDPC decoder decodes the deinterleaved soft bit values and generates hard decisions. The BCH decoder works on these hard decisions to create the final estimate of the received frame.

The second part of the for-loop collects performance measurements such as the bit error rate and a scatter plot. It also estimates the received SNR value.

bbFrameTx = false(encbch.MessageLength,1); numIterVec = zeros(numFrames, 1); falseVec = false(dvb.NumPacketsPerBBFrame, 1); for frameCnt=1:numFrames % Transmitter, channel, and receiver bbFrameTx(1:dvb.NumInfoBitsPerCodeword) = ... logical(randi([0 1], dvb.NumInfoBitsPerCodeword, 1)); bchEncOut = encbch(bbFrameTx); ldpcEncOut = encldpc(bchEncOut); intrlvrOut = intrlvr(ldpcEncOut); modOut = pskModulator(intrlvrOut); chanOut = chan(modOut); demodOut = pskDemodulator(chanOut); deintrlvrOut = deintrlvr(demodOut); [ldpcDecOut, numIter] = decldpc(deintrlvrOut); bchDecOut = decbch(ldpcDecOut); bbFrameRx = bchDecOut(1:dvb.NumInfoBitsPerCodeword,1); % Error statistics comparedBits = xor(bbFrameRx, bbFrameTx(1:dvb.NumInfoBitsPerCodeword)); packetErr = any(reshape(comparedBits, dvb.NumBitsPerPacket, ... dvb.NumPacketsPerBBFrame)); per = PER(falseVec, packetErr'); berMod = BERMod(demodOut<0, intrlvrOut); berLDPC = BERLDPC(ldpcDecOut, bchEncOut); % LDPC decoder iterations numIterVec(frameCnt) = numIter; % Noise variance estimate noiseVar = meanCalc(varCalc(chanOut - modOut)); % Scatter plot constDiag(chanOut); end

The step method of the error rate measurement objects, hPER, hBERMod, and hBERLDPC, outputs a 3-by-1 vector containing updates of the measured error rate value, the number of errors, and the total number of transmissions (packets or bits). Display the BER at the demodulator output, the BER at the LDPC decoder output, and the packet error rate of the end-to-end system together with the measured SNR at the receiver input. While the demodulator output presents an error rate of more than 10%, the LDPC decoder is able to correct all of the errors and provide error free packets.

fprintf('Measured SNR : %1.2f dB\n', 10*log10(1/noiseVar)) fprintf('Modulator BER: %1.2e\n', berMod(1)) fprintf('LDPC BER : %1.2e\n', berLDPC(1)) fprintf('PER : %1.2e\n', per(1))

Measured SNR : 0.99 dB Modulator BER: 1.31e-01 LDPC BER : 0.00e+00 PER : 0.00e+00

The figure shows the distribution of the number of iterations performed by the LDPC decoder. The decoder was able to decode all the frames without an error before reaching the maximum iteration count of 50.

distFig = figure; histogram(numIterVec, 1:decldpc.MaximumIterationCount-1); xlabel('Number of iterations'); ylabel('# occurrences'); grid on; title('Distribution of number of LDPC decoder iterations')

We ran the stream processing loop for 32.4e6 bits for several SNR values. Since this simulation takes a long time, in this example we only provide the result of the simulation stored in a MAT-file.

load berResultsDVBS2Demo.mat cBER snrdb berFig = figure; semilogy(snrdb, cBER(1,:)); xlabel('SNR (dB)'); ylabel('BER'); grid on

This example utilized several System objects to simulate part of the DVB-S.2 communication system over an AWGN channel. It showed how to model several parts of the DVB-S.2 system such as the LDPC coding. System performance was measured using the PER and BER values obtained with error rate measurement System objects.

You can modify parts of this example to experiment with different subsystem types using various values for Es/No and maximum number of LDPC decoder iterations. This example supports the following subsystem types:

'QPSK 1/4', 'QPSK 1/3', 'QPSK 2/5', 'QPSK 1/2', 'QPSK 3/5', 'QPSK 2/3', 'QPSK 3/4', 'QPSK 4/5', 'QPSK 5/6', 'QPSK 8/9', 'QPSK 9/10'

'8PSK 3/5', '8PSK 4/5', '8PSK 2/3', '8PSK 3/4', '8PSK 5/6', '8PSK 8/9', '8PSK 9/10'

This example uses the following scripts and helper function:

ETSI Standard EN 302 307 V1.1.1:

*Digital Video Broadcasting (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications (DVB-S2)*, European Telecommunications Standards Institute, Valbonne, France, 2005-03.R. G. Gallager,

*Low-Density Parity-Check Codes*, IEEE Transactions on Information Theory, Vol. 8, No. 1, January 1962, pp. 21-28.W. E. Ryan,

*An introduction to LDPC codes*, in Coding and Signal Processing for Magnetic Recording Systems (Bane Vasic, ed.), CRC Press, 2004.

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