Binary Symmetric Channel
Introduce binary errors
Libraries:
Communications Toolbox /
Channels
Description
The Binary Symmetric Channel block introduces errors to the input signal transmitted through a binary symmetric channel. The errors are introduced based on the specified Error probability. For more information, see Tips.
Examples
Viterbi Decoding of Binary Symmetric Channel Impaired Data
The cm_ex_viterbi_decode_binary_seq
model generates a binary sequence using the Random Integer Generator
block. The sequence is encoded with the Convolutional Encoder
block and then impaired with the Binary Symmetric Channel
block. The Viterbi Decoder
block decodes the data sequence and the bit error rate is computed.
The InitFcn
callback is used to initialize workspace parameters for samples per frame, BSC error probability, and the Viterbi decoder traceback depth. The signal delay between the transmitted and received signal is equal to the traceback depth. The signal delay is needed for the error rate calculation.
To produce a binary bit stream, the Random Integer Generator
block specifies a set size of 2
, and output type of boolean
.
The computed error rate approximates the Error probability
specified in the Binary Symmetric Channel
block.
Computed error rate = 0.095023
Binary Symmetric Channel Error Rate
Pass a random signal through a binary symmetric channel. Calculate the error rate for specified error probability.
Use the Open model button to open the slex_bsc_channel
model.
Run the model with the error probability of the BSC block set to 0.01. The results are saved to the base workspace variable ErrorVec
in a 1by3 row vector. The first element contains the BER.
With error probability set to 0.01, BER: 0.009929
Change the error probability of the BSC block to 0.04. Run the model and observe the increase in BER.
With error probability set to 0.04, BER: 0.039889
Binary Symmetric Channel Error Port
Pass a random signal through a binary symmetric channel. For a specified error probability, compare the total number of errors indicated by the Err
port to result reported by the Error Rate Calculation
block.
Open the slex_bsc_channel_err
model.
Run the model with the error probability of the BSC block set to 0.02. The results from the Error Rate Calculation
block are saved to the base workspace variable ErrorVec
in a 1by3 row vector. ErrorVec
contains [ BER
, TotalErrors
, TotalSamplesProcessed
].
Total number of errors: 20296
The Err
port for the Binary Symmetric Channel
is a binary vector whose length matches the total number of samples processed. By summing the elements of the output Err
vector you get the total number of errors introduced into the signal data. The sum of the elements of the Err
vector is saved to the base workspace variable BscErrTotal
.
BscErrTotal: 20296
The Error Rate Calculation
blocks reports the same total number of errors indicated by BscErrTotal
.
Vary Probability Error for MultiChannel Binary Symmetric Channel
Pass a multichannel random signal through a binary symmetric channel. For a specified error probability, compare the error rate comparing the Err
port output for each channel.
Use the Open model button to open the slex_multichannel_bcs_err
model.
Set different BSC error probabilities for the individual channels of a multichannel signal by defining the Error probability
as a row vector set to [ 0.02 0.04 0.07
].
The Err
port for the Binary Symmetric Channel
is a binary matrix whose dimensions match the input signal. Err
contains the error results for each channel. Sum the elements of each column output in Err
individually to get the total number of errors introduced per channel. Dividing each total by the total number of samples sent per channel yields the bit error rate for each channel.
BER for channel 1: 2.02960e02 BER for channel 1: 3.97430e02 BER for channel 1: 7.00090e02
The computed BERs are approximately equal to the probabilities set in the Error probability
parameter.
Ports
Input
Input — Input signal
column vector  matrix
Input signal, specified as a column vector or an
N_{S}byN_{C}
matrix of Boolean
values.
N_{S} is the number of
samples per channel. N_{C} is the
number of independent data channels. For more information, see Tips.
Output
Output — Binary output signal
column vector  matrix
Binary output signal, returned as a column vector or matrix with the
same dimensions as Input
. The output signal is a
version of the input signal that has been modified by introducing random
errors based on the specified Error probability. To set the output data type, use Output data type.
Err — Error locations
column vector  matrix
Error locations, returned as a column vector or matrix with the same
dimensions as Input
. Element values in
Err
are 1
or
0
, where:
1
indicates that the corresponding element inOutput
has an error.0
indicates that the corresponding element inOutput
does not have an error.
The data type of Err
is the same as
Output, as set
by Output data type.
Dependencies
To enable this port, select Output error vector.
Parameters
To edit block parameters interactively, use the Property Inspector. From the Simulink^{®} Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.
Error probability — Probability of error occurrence
0.05
(default)  scalar
Probability of error occurrence for the input signal elements, specified as a scalar in the range [0,1]. The probability of error applies independently for each element.
Output error vector — Option to output error locations
on
(default)  off
To enable the Err
output port to the block, select
this parameter.
Output data type — Output data type
double
(default)  single
 boolean
Select the output data type as double
,
single
, or boolean
. This parameter
sets the output data type for both the Output and
Err ports.
Initial seed — Initial seed
71
(default)  integer
Initial seed value for the random number generator used by the block,
specified as an integer. The block uses the mt19937ar
algorithm to generate uniformly distributed random numbers. For details
about the mt19937ar
algorithm, see Creating and Controlling a Random Number Stream.
Simulate using — Type of simulation to run
Code generation
(default)  Interpreted execution
Type of simulation to run, specified as:
Code generation
–– Simulate the model using generated C code. The first time you run a simulation, Simulink generates C code for the block. The C code is reused for subsequent simulations as long as the model does not change. This option requires additional startup time.Interpreted execution
–– Simulate the model using the MATLAB^{®} interpreter. This option shortens startup time. InInterpreted execution
mode, you can debug the source code of the block.
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

Tips
When the input consists of not
Boolean
values, Binary Symmetric Channel converts zerovalued elements to 0 and converts nonzerovalued elements to 1.The Binary Symmetric Channel block creates and uses an independent
RandStream
to provide a random number stream for probability determination.To generate repeatable results, use the same Initial seed value.
To generate independent probability statistics, set different Initial seed values for multichannel signals, multiple processing chains, or simulation runs.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced before R2006aR2018b: Random Number Generation
To improve statistical properties, the Binary Symmetric Channel block uses the
mt19937ar
algorithm with RandStream
. The Binary Symmetric Channel block accepts a single scalar value for
the Initial seed parameter.
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