BCH Decoder
Decode BCH code to recover binary vector data
 Library:
Communications Toolbox / Error Detection and Correction / Block
Description
The BCH Decoder block recovers a binary message vector from a binary BCH codeword vector. For proper decoding, the Codeword length, N and Message length, K parameter values in this block must match the parameters in the corresponding BCH Encoder block. The fulllength values of N and K must produce a valid narrowsense BCH code.
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.
If decoding fails, the message portion of the decoder input is returned unchanged as the decoder output.
The sample times of all input and output signals are equal.
This icon shows optional ports.
Ports
Input
In
— Encoded message
binary column vector
Encoded message, specified 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
Era
— Erasure vector
binary column vector
Erasure vector, specified as a binary column vector that is the same
length as In
. Erasure values of 1 correspond to
erased bits in the same position in the codeword. Values of 0 correspond
to bits that are not erased.
Dependencies
To enable this port, select Enable erasures input port.
Data Types: double
 Boolean
Output
Out
— Decoded message
binary column vector
Decoded message, returned 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 codeword to decode. The input and output signal lengths are listed in the Input and Output Signal Length in BCH Blocks table.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
Err
— Decoding errors
integer vector
Decoding errors, returned as an integer vector that indicates the number of errors detected during decoding of the codeword. A negative integer indicates that the block detected more errors than it could correct by using the coding scheme.
Dependencies
To enable this port, select Output number of corrected errors.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
For more information, see Supported Data Types.
Parameters
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)  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 Puncturing and Erasures.
Dependencies
To enable this parameter, select Puncture code.
Enable erasures input port
— Option to enable erasures input port
off (default)  on
Selecting this check box enables the erasures port,
Era
.
Through the port, you can input a binary column vector that is 1/M times as long as the codeword input.
Erasure values of 1
correspond to erased symbols in the
same position in the bitpacked codeword. Values of 0
correspond to nonerased symbols. For more information, see Puncturing and Erasures.
Output number of corrected errors
— Option to enable port to output number of corrected errors
off (default)  on
Selecting this check box enables an additional output port,
Err
, which indicates the number of errors the block
corrected in the input codeword.
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.
Puncturing and Erasures
1
s and 0
s have
precisely opposite meanings for the puncture and erasure vectors.
In a puncture vector,
1
means that the data symbol is passed through the block unaltered.0
means that the data symbol is to be punctured, or removed, from the data stream.
In an erasure vector,
1
means that the data symbol is to be replaced with an erasure symbol.0
means that the data symbol is passed through the block unaltered.
These conventions apply to both the encoder and the decoder. For more information, see Shortening, Puncturing, and Erasures.
Supported Data Types
Port  Supported Data Types 

In 

Out 

Era 

Err 

Pair Block
BCH Encoder — Encodes data using BCH algorithm.
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] Wicker, Stephen B. Error Control Systems for Digital Communication and Storage. Upper Saddle River, NJ: Prentice Hall, 1995.
[2] Berlekamp, Elwyn R. Algebraic Coding Theory. New York: McGrawHill, 1968.
[3] 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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