The DVB-S system is used for satellite television signal transmission, and the block diagram of the transmitter is shown below.
Scrambling#
In practical digital communication, the payload data can have long runs of 0s or 1s, which is detrimental to the receiver's ability to extract the clock signal. This also results in a large number of low-frequency components in the data stream, causing the phase of the QPSK modulator to remain unchanged for extended periods, making the signal susceptible to interference. Therefore, scrambling is applied to the payload data.
The DVB-S standard specifies the polynomial for scrambling generation as
The initial state of the shift register is "1001_0101_0000_000”.
Matlab Code Simulation#
n=500;
% origin_data=randi([0 1],n,1);
origin_cnt_1=nnz(origin_data==1)
scrambling = comm.Scrambler("CalculationBase",2,"InitialConditions",[1 0 0 1 0 1 0 1 0 0 0 0 0 0 0], ...
"Polynomial",[1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]);
scrambling_data=step(scrambling,origin_data);
scrambling_data_cnt_1=nnz(scrambling_data==1)
The results are shown in the figure below.
It can be seen that in the initial data packet of 500 points, there are 403 "1s", and after scrambling, the number of "1s" is close to half of the total data.
Outer Error Correction Coding (RS Coding)#
RS Code Definition:
$GF(q)$ (where $q \neq 2$, usually $q=2^m$) is a primitive BCH code of length $n=q-1$.
The parameters of the RS code that can correct $t$ errors are:
- Block length $n=q-1$
- Number of check symbols $n-k=2t$
- Minimum distance of the code $d_{min}=2t+1$
The RS(188, 204) used in the DVB-S system is truncated from RS(239, 255) and can correct 8 bytes of errors.
Matlab Simulation#
m=8; %bit per symbol
n=204;
k=188;
data_test=randi([0,n],1,k);
data_gf=gf(data_test,m);
data_rs_enc=rsenc(data_gf,n,k);
data_enc=data_rs_enc.x;
data_rs_dec=rsdec(data_rs_enc,n,k);
data_dec=data_rs_dec.x;
subplot(3,1,1);
stem(data_test);
subplot(3,1,2);
stem(data_enc);
subplot(3,1,3);
stem(data_dec);
First, a sequence of length 188 is generated, converted to the Galois field, and then RS encoding is performed using the rsenc function, followed by decoding. A comparison shows that the bits after decoding are exactly the same as before decoding.
Convolution Interleaving#
In actual transmission, factors such as pulse interference and multipath effects can cause sustained burst errors. Although RS codes have good error correction capabilities for burst errors, when the duration is too long, it exceeds the correction capability of the RS code. Therefore, convolution interleaving is introduced during encoding to disperse the transmission order of the data according to a certain pattern, which can also disperse the erroneous symbols.
In DVB-S, the interleaving depth is 12, with a total of 17 FIFOs. Data is written into the register by rows and read out by columns.
The maximum correctable length after interleaving is $12*8=96$.
It can be seen that a lot of 0s were read during the previous period, indicating that the data in the shift register below has not yet moved to the end.
Convolution Coding#
Convolutional codes are an effective forward error correction code denoted as $(n,k,m)$, encoding $k$ information bits into $n$ bits, where $m$ is the encoding memory length, and $N=m+1$ is the constraint length. This means that the current coded symbol depends not only on the current input of $k$ information symbols but also on the previous $m$ time inputs of information symbols.
clc;
close all;
n=500;
tre1=[1 1 1 1 0 0 1]; %oct 171
tre2=[1 0 1 1 0 1 1]; %oct 133
trellis = poly2trellis(7,[171 133]);
convData=convenc(scrambling_data,trellis);
decData=vitdec(convData,trellis,499,"trunc","hard");
subplot(3,1,1);
stem(scrambling_data);
subplot(3,1,2);
stem(convData);
subplot(3,1,3);
stem(decData);
biterr(scrambling_data,decData)
Using poly2trellis, the convolution encoding polynomial is converted into a trellis description.
A comparison shows that the decoded data is exactly the same as the original data.