comm.BCHEncoder

Encode data using BCH encoder

Description

The comm.BCHEncoder System object™ creates a BCH code with message and codeword lengths that you specify. For more information, see Algorithms.

To encode data using a BCH-coding scheme:

Create the comm.BCHEncoder object and set its properties.
Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

enc = comm.BCHEncoder

enc = comm.BCHEncoder(N,K)

enc = comm.BCHEncoder(N,K,GP)

enc = comm.BCHEncoder(N,K,GP,S)

enc = comm.BCHEncoder(___,Name=Value)

Description

enc = comm.BCHEncoder creates a BCH encoder System object, enc, that applies BCH encoding.

example

enc = comm.BCHEncoder(N,K) sets CodewordLength to N and MessageLength to K. For example, comm.BCHEncoder(7,3) creates a (7,3) BCH encoder object.

enc = comm.BCHEncoder(N,K,GP) additionally sets GeneratorPolynomial to GP and GeneratorPolynomialSource to 'Property'.

enc = comm.BCHEncoder(N,K,GP,S) additionally sets ShortMessageLength to S and ShortMessageLengthSource to 'Property'.

example

enc = comm.BCHEncoder(___,Name=Value) specifies options using one or more name-value arguments in addition to the input arguments in previous syntaxes. For example, comm.BCHEncoder(7,3,PuncturePatternSource="Property",PuncturePattern=[ones(7,1); zeros(3,1)]) creates a (7, 3) BCH encoder object with the puncture pattern set to [1;1;1;1;1;1;1;0;0;0].

Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`CodewordLength` — Codeword length of BCH code
`15` (default) | positive integer

Codeword length of the BCH code in symbols, specified as a positive integer. The values of the CodewordLength and MessageLength properties must produce a valid narrow-sense BCH code. For a full-length BCH code, the value of this property must take the form (2^M – 1), where M is an integer in the range [3, 16].

`MessageLength` — Message length
`5` (default) | positive integer

Message length in symbols, specified as a positive integer. The values of the CodewordLength and MessageLength properties must produce a valid narrow-sense BCH code.

`ShortMessageLengthSource` — Source of short message length
`"Auto"` (default) | `"Property"`

Source of the short message length, specified as "Auto" or "Property".

When you set this property to "Auto", the object derives the shortening from CodewordLength and MessageLength. The object defines the BCH code based on the CodewordLength, MessageLength, GeneratorPolynomial, and PrimitivePolynomial properties.
When you set this property to "Property", the object uses ShortMessageLength along with the other properties to define the BCH code.

`ShortMessageLength` — Shortened message length
`5` (default) | positive integer

Shortened message length in symbols, specified as a positive integer whose value must be less than or equal to MessageLength. When ShortMessageLength < MessageLength, the object shortens the BCH code.

Dependencies

This property applies when you set ShortMessageLengthSource to "Property".

`GeneratorPolynomialSource` — Source of generator polynomial
`"Auto"` (default) | `"Property"`

Source of the generator polynomial, specified as "Auto" or "Property".

When you set this property to "Auto", the object calculates the generator polynomial based on the value of PrimitivePolynomial.
When you set this property to "Property", the object uses GeneratorPolynomial to define the generator polynomial.

`GeneratorPolynomial` — Generator polynomial
`'X^10 + X^8 + X^5 + X^4 + X^2 + X + 1'` (default) | integer row vector | `gf` row vector | character vector | string scalar

Generator polynomial, specified as a polynomial string, integer row vector, or Galois field row vector. The specified row vector defines the finite field gf(2^M) in descending order of powers corresponding to the integers that form messages and codewords. The length of the generator polynomial must be (N – K + 1), where N is CodewordLength and K is MessageLength.

Express the polynomial as one of these options:

Character vector or string scalar of a polynomial whose constant term is 1. For more information, see Representation of Polynomials in Communications Toolbox.
Binary-valued row vector that represents the coefficients of the polynomial in order of descending powers. The length of this vector must be (M + 1), where M is the degree of the polynomial. The first and last entries must be 1, indicating the leading term with degree M and a constant term of 1.
Integer-valued row vector of elements that represent the exponents for the nonzero terms of the polynomial in order of descending powers. The last entry must be 0, indicating a constant term of 1.

The default 'X^10 + X^8 + X^5 + X^4 + X^2 + X + 1' the result of bchgenpoly(15,5,[],'double') and corresponds to a (15,5) code.

Dependencies

This property applies when you set GeneratorPolynomialSource to "Property".

Data Types: double | string | char

`CheckGeneratorPolynomial` — Option to check generator polynomial
`true` or `1` (default) | `false` or `0`

Option to check the generator polynomial, specified as a logical 1 (true) or 0 (false). Set this property to true to verify the specified generator polynomial is valid.

Tips

For codes with generator polynomials of high degree, disabling the check speeds up processing. As a best practice, perform the check at least once before setting this property to false.

Dependencies

This property applies when GeneratorPolynomialSource is set to "Property".

Data Types: logical

`PrimitivePolynomialSource` — Source of primitive polynomial
`"Auto"` (default) | `"Property"`

Source of the primitive polynomial, specified as "Auto" or "Property".

When you set this property to "Auto", the object uses a primitive polynomial of degree M = ceil(log2(CodewordLength + 1)).
When you set this property to "Property", the object uses PrimitivePolynomial to define the primitive polynomial.

`PrimitivePolynomial` — Primitive polynomial
`'X^4 + X + 1'` (default) | character vector | string scalar | binary row vector

Primitive polynomial, specified as a binary row vector that defines the finite field gf(2^M) in descending order of powers corresponding to the integers that form messages and codewords.

Express the polynomial as one of these options:

Character vector or string scalar of a polynomial whose constant term is 1. For more information, see Representation of Polynomials in Communications Toolbox.
Binary-valued row vector that represents the coefficients of the polynomial in order of descending powers. The length of this vector must be M + 1, where M is the degree of the polynomial. The first and last entries must be 1, indicating the leading term with degree M and a constant term of 1.
Integer-valued row vector of elements that represent the exponents for the nonzero terms of the polynomial in order of descending powers. The last entry must be 0, indicating a constant term of 1.

The default 'X^4 + X + 1' is the result of int2bit(primpoly(4),5)'.

Dependencies

This property applies when you set PrimitivePolynomialSource to "Property".

`PuncturePatternSource` — Source of puncture pattern
`"None"` (default) | `"Property"`

Source of the puncture pattern, specified as "None" or "Property".

When you set this property to "None", the object does not apply puncturing to the code.
When you set this property to "Property", the object punctures the code using the puncture pattern vector defined by PuncturePattern.

`PuncturePattern` — Puncture pattern
`[ones(8,1); zeros(2,1)]` (default) | binary column vector

Puncture pattern, specified as a binary column vector with a length of (N – K), where N is CodewordLength and K is MessageLength. Zeros in the puncture pattern vector indicate the position of the parity symbols that are punctured or excluded from each codeword.

Dependencies

This property applies when you set PuncturePatternSource to "Property".

Usage

Syntax

Y = enc(X)

Description

Y = enc(X) encodes the input message using a (CodewordLength,MessageLength) BCH encoder with the corresponding narrow-sense generator polynomial. For information about the input and output lengths when you run the object, see Input and Output Signal Lengths in BCH and RS System Objects.

example

Input Arguments

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`X` — Message to encode
column vector

Message to encode, specified as numeric or logical column vector with length equal to an integer multiple of MessageLength. A group of MessageLength input elements represents one message word to be encoded.

Output Arguments

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`Y` — BCH-encoded codeword
binary-valued column vector

BCH-encoded codeword, returned as a binary-valued column vector. The length of the encoded data output vector is an integer multiple of (CodewordLength – N_punctures), where N_punctures is the number of punctures. You specify the number of punctures with the PuncturePatternSource and PuncturePattern properties.

Data Types: single | logical

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

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Common to All System Objects

`step`	Run System object algorithm
`release`	Release resources and allow changes to System object property values and input characteristics
`reset`	Reset internal states of System object

Examples

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Compute Errors for 8-DPSK-Modulated Signal with BCH Forward Error Correction Applied

Open Live Script

Transmit a BCH-encoded, 8-DPSK-modulated bit stream through an AWGN channel, and then demodulate, decode, and count errors in the received signal.

enc = comm.BCHEncoder;
mod = comm.DPSKModulator(BitInput=true);
snr = 10;
demod = comm.DPSKDemodulator(BitOutput=true);
dec = comm.BCHDecoder;
errorRate = comm.ErrorRate(ComputationDelay=3);

for counter = 1:20
  data = randi([0 1],30,1);
  encodedData = enc(data);
  modSignal = mod(encodedData);
  receivedSignal = awgn(modSignal,snr);
  demodSignal = demod(receivedSignal);
  receivedBits = dec(demodSignal);
  errorStats = errorRate(data,receivedBits);
end
fprintf('Error rate = %f\nNumber of errors = %d\n', ...
  errorStats(1),errorStats(2))

Error rate = 0.008375
Number of errors = 5

Shorten BCH Code

Open Live Script

Shorten a (31,26) BCH code to an (11,6) BCH code and use it to encode and decode random binary data.

Create a BCH encoder and decoder pair for a (31,26) code. Specify the generator polynomial, $x^{5} + x^{2} + 1$ , and a shortened message length of 6.

N = 31;        % Codeqword length
K = 26;        % Message length
S = 6;         % Shortened message length
gp = 'x5+x2+1' % Generator polynomial

gp = 
'x5+x2+1'

enc = comm.BCHEncoder(N,K,gp,S);
dec = comm.BCHDecoder(N,K,gp,S);

Encode and decode random binary data and verify that the decoded bit stream matches the original data.

X = randi([0 1],60,1);
Y = enc(X);
Z = dec(Y);
isequal(X,Z)

ans = logical
   1

Transmit and Receive BCH-Coded and BPSK-Modulated Signal

Open Live Script

Transmit and receive a BPSK-modulated signal encoded with a shortened BCH code, then count errors.

Define variables for coding configuration based on the AMR standard.

N = 255;              % Codeword length
K = 239;              % Message length
S = 63;               % Shortened message length
gp = bchgenpoly(N,K); % BCH (255,239) generator polynomial

Create a BCH encoder and decoder pair.

bchEncoder = comm.BCHEncoder(N,K,gp,S);
bchDecoder = comm.BCHDecoder(N,K,gp,S);

Create an error rate counter.

errorRate = comm.ErrorRate('ComputationDelay',3);

Run the main processing loop.

snr = 5;
for counter = 1:20
  data = randi([0 1],630,1);                 % Generate binary data
  encodedData = bchEncoder(data);            % BCH encode data
  modSignal = pskmod(encodedData,2);         % BPSK modulate
  receivedSignal = awgn(modSignal,snr);      % Pass through AWGN channel
  demodSignal = pskdemod(receivedSignal,2);  % BSPK demodulate
  receivedBits = bchDecoder(demodSignal);    % BCH decode data
  errorStats = errorRate(data,receivedBits); % Compute error statistics
end

Display the error statistics.

fprintf('Error rate = %f\nNumber of errors = %d\n', ...
  errorStats(1),errorStats(2))

Error rate = 0.000238
Number of errors = 3

Algorithms

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This object implements Bose-Chaudhuri-Hocquenghem (BCH) coding as described in [1] and Algorithms for BCH and RS Errors-only Decoding.

Input and Output Signal Lengths in BCH and RS System Objects

The notation y = c * x denotes that y is an integer multiple of x.

The number of punctures equals the number of zeros in the puncture vector.

M is the degree of the primitive polynomial. Each group of M bits represents an integer in the range [0, (2^M–1)] that belongs to the finite Galois field gf(2^M).

ShortMessageLengthSource "Auto" "Property"

`ShortMessageLengthSource`	`"Auto"`	`"Property"`
`comm.BCHEncoder` and `comm.RSEncoder(BitInput=false)`	Input Length: `c * MessageLength` Output Length: `c * (CodewordLength – number of punctures)`	Input Length: `c * ShortMessageLength` Output Length: `c * (CodewordLength - MessageLength + ShortMessageLength - number of punctures)`
`comm.BCHDecoder` and `comm.RSDecoder(BitInput=false)`	Input Length: `c * (CodewordLength – number of punctures)` Output Length: `c * MessageLength` Erasures Length: `c * (CodewordLength – number of punctures)`	Input Length: `c * (CodewordLength - MessageLength + ShortMessageLength - number of punctures)` Output Length: `c * ShortMessageLength` Erasures Length: `c * (CodewordLength - MessageLength + ShortMessageLength - number of punctures)`
`comm.RSEncoder(BitInput=true)`	Input Length: `c * (MessageLength * M)` Output Length: `c * ((CodewordLength – number of punctures) * M)`	Input Length: `c * (ShortMessageLength * M)` Output Length: `c * ((CodewordLength - MessageLength + ShortMessageLength - number of punctures) * M)`
`comm.RSDecoder(BitInput=true)`	Input Length: `c * ((CodewordLength – number of punctures) * M)` Output Length: `c * (MessageLength * M)` Erasures Length: `c * (CodewordLength – number of punctures)`	Input Length: `c * ((CodewordLength - MessageLength + ShortMessageLength - number of punctures) * M)` Output Length: `c * (ShortMessageLength * M)` Erasures Length: `c * (CodewordLength - MessageLength + ShortMessageLength - number of punctures)`

comm.BCHEncoder

and

comm.RSEncoder(BitInput=false)

Input Length:

c * MessageLength

Output Length:

c * (CodewordLength – number of punctures)

Input Length:

c * ShortMessageLength

Output Length:

c * (CodewordLength - MessageLength + ShortMessageLength - number of punctures)

comm.BCHDecoder

and

comm.RSDecoder(BitInput=false)

Input Length:

c * (CodewordLength – number of punctures)

Output Length:

c * MessageLength

Erasures Length:

c * (CodewordLength – number of punctures)

Input Length:

c * (CodewordLength - MessageLength + ShortMessageLength - number of punctures)

Output Length:

c * ShortMessageLength

Erasures Length:

c * (CodewordLength - MessageLength + ShortMessageLength - number of punctures)

comm.RSEncoder(BitInput=true)

Input Length:

c * (MessageLength * M)

Output Length:

c * ((CodewordLength – number of punctures) * M)

Input Length:

c * (ShortMessageLength * M)

Output Length:

c * ((CodewordLength - MessageLength + ShortMessageLength - number of punctures) * M)

comm.RSDecoder(BitInput=true)

Input Length:

c * ((CodewordLength – number of punctures) * M)

Output Length:

c * (MessageLength * M)

Erasures Length:

c * (CodewordLength – number of punctures)

Input Length:

c * ((CodewordLength - MessageLength + ShortMessageLength - number of punctures) * M)

Output Length:

c * (ShortMessageLength * M)

Erasures Length:

c * (CodewordLength - MessageLength + ShortMessageLength - number of punctures)

References

[1] Clark, George C., and J. Bibb Cain. Error-Correction Coding for Digital Communications. Applications of Communications Theory. New York: Plenum Press, 1981.

[2] Wicker, Stephen B. Error Control Systems for Digital Communication and Storage. Upper Saddle River, NJ: Prentice Hall, 1995.

Extended Capabilities

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

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

When you use this object to generate code, you must set the generator polynomial to a double-precision integer row vector.

Version History

Introduced in R2012a

comm.BCHEncoder

Description

Creation

Syntax

Description

Properties

CodewordLength — Codeword length of BCH code 15 (default) | positive integer

MessageLength — Message length 5 (default) | positive integer

ShortMessageLengthSource — Source of short message length "Auto" (default) | "Property"

ShortMessageLength — Shortened message length 5 (default) | positive integer

Dependencies

GeneratorPolynomialSource — Source of generator polynomial "Auto" (default) | "Property"

GeneratorPolynomial — Generator polynomial 'X^10 + X^8 + X^5 + X^4 + X^2 + X + 1' (default) | integer row vector | gf row vector | character vector | string scalar

Dependencies

CheckGeneratorPolynomial — Option to check generator polynomial true or 1 (default) | false or 0

Tips

Dependencies

PrimitivePolynomialSource — Source of primitive polynomial "Auto" (default) | "Property"

PrimitivePolynomial — Primitive polynomial 'X^4 + X + 1' (default) | character vector | string scalar | binary row vector

Dependencies

PuncturePatternSource — Source of puncture pattern "None" (default) | "Property"

PuncturePattern — Puncture pattern [ones(8,1); zeros(2,1)] (default) | binary column vector

Dependencies

Usage

Syntax

Description

Input Arguments

X — Message to encode column vector

Output Arguments

Y — BCH-encoded codeword binary-valued column vector

Object Functions

Common to All System Objects

Examples

Compute Errors for 8-DPSK-Modulated Signal with BCH Forward Error Correction Applied

Shorten BCH Code

Transmit and Receive BCH-Coded and BPSK-Modulated Signal

Algorithms

Input and Output Signal Lengths in BCH and RS System Objects

References

Extended Capabilities

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

Version History

See Also

Objects

Functions

`CodewordLength` — Codeword length of BCH code
`15` (default) | positive integer

`MessageLength` — Message length
`5` (default) | positive integer

`ShortMessageLengthSource` — Source of short message length
`"Auto"` (default) | `"Property"`

`ShortMessageLength` — Shortened message length
`5` (default) | positive integer

`GeneratorPolynomialSource` — Source of generator polynomial
`"Auto"` (default) | `"Property"`

`GeneratorPolynomial` — Generator polynomial
`'X^10 + X^8 + X^5 + X^4 + X^2 + X + 1'` (default) | integer row vector | `gf` row vector | character vector | string scalar

`CheckGeneratorPolynomial` — Option to check generator polynomial
`true` or `1` (default) | `false` or `0`

`PrimitivePolynomialSource` — Source of primitive polynomial
`"Auto"` (default) | `"Property"`

`PrimitivePolynomial` — Primitive polynomial
`'X^4 + X + 1'` (default) | character vector | string scalar | binary row vector

`PuncturePatternSource` — Source of puncture pattern
`"None"` (default) | `"Property"`

`PuncturePattern` — Puncture pattern
`[ones(8,1); zeros(2,1)]` (default) | binary column vector

`X` — Message to encode
column vector

`Y` — BCH-encoded codeword
binary-valued column vector

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