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 full-length values of N and K must produce a valid narrow-sense 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 error-correcting 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

expand all

`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).

`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

expand all

`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.

`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.

For more information, see Supported Data Types.

Parameters

expand all

`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 Character Representation of Polynomials.
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 Character Representation of Polynomials.
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, de2bi(primpoly(4,'nodisplay'),'left-msb')

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 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 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 bit-packed 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.

Model 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.

Block Characteristics

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

More About

expand all

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

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)*

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)

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.

Puncturing and Erasures

1s and 0s 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	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
Era	Double-precision floating point Boolean
Err	Double-precision floating point Boolean 8-, 16-, and 32-bit signed integers 8-, 16-, and 32-bit unsigned integers

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 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] 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: McGraw-Hill, 1968.

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

Documentation

BCH Decoder

Description

Ports

Input

In — Encoded message binary column vector

Era — Erasure vector binary column vector

Dependencies

Output

Out — Decoded message binary column vector

Err — Decoding errors integer vector

Dependencies

Parameters

Codeword length, N — Codeword length 15 (default) | integer

Message length, K — Message length 5 (default) | integer

Shortened message length, S — Shortened message length 5 (default) | integer

Dependencies

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

Dependencies

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

Dependencies

Disable generator polynomial checking — Option to disable generator polynomial checking on (default) | off

Dependencies

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

Dependencies

Enable erasures input port — Option to enable erasures input port off (default) | on

Output number of corrected errors — Option to enable port to output number of corrected errors off (default) | on

Model Examples

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

Block Characteristics

More About

Input and Output Signal Length in BCH Blocks

Puncturing and Erasures

Supported Data Types

Pair Block

Tips

Algorithms

References

Extended Capabilities

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

See Also

Blocks

Objects

Functions

Topics

Communications Toolbox Documentation

Support

`In` — Encoded message
binary column vector

`Era` — Erasure vector
binary column vector

`Out` — Decoded message
binary column vector

`Err` — Decoding errors
integer vector

`Codeword length, N` — Codeword length
`15` (default) | integer

`Message length, K` — Message length
`5` (default) | integer

`Shortened message length, S` — Shortened message length
`5` (default) | integer

`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

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

`Disable generator polynomial checking` — Option to disable generator polynomial checking
on (default) | off

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

`Enable erasures input port` — Option to enable erasures input port
off (default) | on

`Output number of corrected errors` — Option to enable port to output number of corrected errors
off (default) | on

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