Binary Symmetric Channel

Introduce binary errors

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  • Binary Symmetric Channel block

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

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This example uses:

Open Model

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

This example uses:

Open Model

Pass a random signal through a binary symmetric channel (BSC), and then calculate the error rate to confirm the specified error probability matches the computed error rate.

The slex_bsc_channel model calculates the bit error rate (BER) of the BSC for the specified error propability and displays the results.

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 1-by-3 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

This example uses:

Open Model

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.

The slex_bsc_channel_err model calculates the error rate of the BSC for the specified error propability and displays the results.

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 1-by-3 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.

This example uses:

Open Model

Pass a multi-channel random signal through a binary symmetric channel (BSC). For a specified error probability, compare the error rate comparing the Err port output for each channel.

The slex_multichannel_bcs_err model passes a multi-channel through a BSC block and cocmpares the error rate for each channel.

Set different BSC error probabilities for the individual channels of a multi-channel 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: 2.02960e-02
BER for channel 1: 3.97430e-02
BER for channel 1: 7.00090e-02

The computed BERs are approximately equal to the probabilities set in the Error probability parameter.

Ports

Input

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Input signal, specified as a column vector or an NS-by-NC matrix of Boolean values. NS is the number of samples per channel. NC is the number of independent data channels. For more information, see Tips.

Output

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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.

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 in Output has an error.

  • 0 indicates that the corresponding element in Output 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

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To edit block parameters interactively, use the Property Inspector. From the Simulink® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

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.

To enable the Err output port to the block, select this parameter.

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 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.

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. In Interpreted execution mode, you can debug the source code of the block.

Block Characteristics

Data Types

Boolean | double | fixed point | integer | single

Multidimensional Signals

no

Variable-Size Signals

no

Tips

  • When the input consists of not Boolean values, Binary Symmetric Channel converts zero-valued elements to 0 and converts nonzero-valued 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

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C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a

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See Also

Blocks

Topics