BCH Encoder
Create BCH code from binary vector data
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 errorcorrecting capabilities for a given BCH code.
Examples
DVBS.2 Link, Including LDPC Coding in Simulink
The stateoftheart channel coding scheme used in the second generation Digital Video Broadcasting standard (DVBS.2), which is deployed by DIRECTV in the United States. The coding scheme is based on concatenation of LDPC (LowDensity ParityCheck) 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 lowcomplexity iterative decoding algorithm. The outer BCH codes are used to correct sporadic errors made by the LDPC decoder.
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 narrowsense 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 fulllength 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 1
s
represent data symbol indices that pass through the block unaltered. Element indices
with 0
s represent data symbol indices that get punctured, or removed,
from the data stream. For more information, see Shortening, Puncturing, and Erasures.
Note
1
s and 0
s 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 

Multidimensional Signals 

VariableSize Signals 

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
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 

Out 

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 errorcorrection capability, runbchnumerr
(N
).Valid values for
N
= 2^{M}–1, where M is an integer from 3 through 16. The maximum allowable value ofN
is 65,535.
Algorithms
This block implements the algorithm, inputs, and outputs described in Algorithms for BCH and RS Errorsonly Decoding.
References
[1] Clark, George C., Jr., and J. Bibb Cain. ErrorCorrection 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
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