BCH Encoder

Create BCH code from binary vector data

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Libraries:
Communications Toolbox / Error Detection and Correction / Block

Description

The BCH Encoder block creates a BCH code with message length K and codeword length (N – number of punctures).

If the encoder is processing multiple codewords per frame, then the same puncture pattern holds for all codewords. The input and output signal lengths are listed in Input and Output Signal Length in BCH Blocks.

See Tips for information about valid N values, valid (N,K) pairs, and error-correcting capabilities for a given BCH code.

Examples

DVB-S.2 Link, Including LDPC Coding in Simulink

The state-of-the-art channel coding scheme used in the second generation Digital Video Broadcasting standard (DVB-S.2), which is deployed by DIRECTV in the United States. The coding scheme is based on concatenation of LDPC (Low-Density Parity-Check) and BCH codes. 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. The outer BCH codes are used to correct sporadic errors made by the LDPC decoder.

• Open Model

Ports

Input

In — Message to encode

binary column vector

Message to encode, specified as a binary column vector input signal with an integer multiple of Message length, K elements or Shortened message length, S elements if the code is shortened. Each group of input elements represents one message word to encode. The input and output signal lengths are listed in Input and Output Signal Length in BCH Blocks.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

Output

Out — Encoded message

binary column vector

Encoded message, returned as a binary column vector. The encoded message is a BCH code with message length K and codeword length (N – number of punctures).

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

For more information, see Supported Data Types.

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.

Codeword length, N — Codeword length

15 (default) | integer

Codeword length, specified as an integer of the form N = 2^M–1, where M is an integer from 3 through 16. For more information, see Tips.

Message length, K — Message length

5 (default) | integer

Message length, specified as an integer. The (N, K) pair must produce a narrow-sense BCH code.

Shortened message length, S — Shortened message length

5 (default) | integer

Shortened message length, specified as an integer. When you specify this parameter, provide full-length N and K values to specify the (N, K) code that is shortened to an (N–K+S, S) code.

Dependencies

To enable this parameter, select Specify shortened message length.

Generator polynomial — Generator polynomial

'X^10 + X^8 + X^5 + X^4 + X^2 + X + 1' (default) | polynomial character vector | binary row vector | binary Galois row vector

Generator polynomial, specified as one of the following:

• A polynomial character vector — For more information, see Representation of Polynomials in Communications Toolbox.

• A binary row vector that represents the coefficients of the generator polynomial in order of descending power.

• A binary Galois row vector that represents the coefficients of the generator polynomial in order of descending power.

Example: 'X^10 + X^8 + X^5 + X^4 + X^2 + X + 1', which is equivalent to bchgenpoly(15,5)

Dependencies

To enable this parameter, select Specify generator polynomial.

Primitive polynomial — Primitive polynomial

'X^4 + X + 1' (default) | polynomial character vector | binary row vector

Primitive polynomial in order of descending power. It is a polynomial of order M that defines the finite Galois field GF(2), specified as one of the following:

• A polynomial character vector — For more information, see Representation of Polynomials in Communications Toolbox.

• A binary row vector that represents the coefficients of the generator polynomial in order of descending power.

Example: 'X^4 + X + 1', which is the primitive polynomial used for a (15,5) code, ppoly = primpoly(4,'nodisplay'); int2bit(ppoly,ceil(log2(max(ppoly))))'

Dependencies

To enable this parameter, select Specify primitive polynomial.

Disable generator polynomial checking — Option to disable generator polynomial checking

on (default) | off

Select this parameter to disable generator polynomial check.

Each time a model initializes, the block performs a polynomial check. This check verifies that X ^N + 1 is divisible by the specified generator polynomial, where N represents the full codeword length. For larger codes, disabling the check speeds up the simulation process.

Tip

Always run the check at least once before disabling this feature.

Dependencies

To enable this parameter, select Specify generator polynomial.

Puncture vector — Puncture vector

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

Puncture vector, specified as a binary column vector of length N–K. Element indices with 1s represent data symbol indices that pass through the block unaltered. Element indices with 0s represent data symbol indices that get punctured, or removed, from the data stream. For more information, see Shortening, Puncturing, and Erasures.

Note

1s and 0s have precisely opposite meanings for the puncture and erasure vectors. For an erasure vector, 1 means that the data symbol is to be replaced with an erasure symbol, and 0 means that the data symbol is passed through the block unaltered. This convention applies to both the encoder and the decoder.

Dependencies

To enable this parameter, select Puncture code.

Block Characteristics

Data Types	Boolean | double | integer | single
Multidimensional Signals	no
Variable-Size Signals	no

More About

Input and Output Signal Length in BCH Blocks

This table shows how to compute the input and output signal lengths for the BCH encoder and decoder blocks.

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

Specify Shortened Message Length, S	BCH Encoder	BCH Decoder
off	Input Length: c * K Output Length: c * (N – P)	Input Length: c * (N – P) Output Length: c * K Erasures Length: c * (N – P)
on	Input Length: c * S Output Length: c * (N - K + S - P)	Input Length: c * (N - K + S - P) Output Length: c * S Erasures Length: c * (N - K + S - P)

• N is the codeword length

• K is the message length

• S is the shortened message length

• P is the number of punctures value, and is equal to the number of zeros in the puncture vector.

Supported Data Types

Port	Supported Data Types
In	Double-precision floating point Boolean 8-, 16-, and 32-bit signed integers 8-, 16-, and 32-bit unsigned integers
Out	Double-precision floating point Boolean 8-, 16-, and 32-bit signed integers 8-, 16-, and 32-bit unsigned integers

Pair Block

BCH Decoder — Decodes BCH encoded data.

Tips

• To generate the list of valid (N,K) pairs along with the corresponding values of the error-correction capability, run bchnumerr(N).

• Valid values for N = 2^M–1, where M is an integer from 3 through 16. The maximum allowable value of N is 65,535.

Algorithms

This block implements the algorithm, inputs, and outputs described in Algorithms for BCH and RS Errors-only Decoding.

References

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

Extended Capabilities

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

Version History

Introduced before R2006a