gen2par

Convert between parity-check and generator matrices

Syntax

``H = gen2par(G) ``
``G = gen2par(H) ``

Description

example

````H = gen2par(G) ` converts a standard-form binary generator matrix to the corresponding parity-check matrix.```

example

````G = gen2par(H) ` converts a standard-form binary parity-check matrix to the corresponding generator matrix.```

Examples

collapse all

Convert the parity-check matrix for a Hamming code into the corresponding generator matrix and back again.

Create the parity-check matrix.

`parmat = hammgen(3)`
```parmat = 3×7 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 ```

Convert the parity-check matrix into the corresponding generator matrix.

`genmat = gen2par(parmat)`
```genmat = 4×7 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 ```

Convert the generator matrix back again. The output, `parmat2`, should be the same as the original matrix, `parmat`.

`parmat2 = gen2par(genmat)`
```parmat2 = 3×7 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 ```

Input Arguments

collapse all

Generator matrix, specified as a k-by-n matrix of binary values. The standard form of a generator matrix for a [n,k] binary linear block code is [Ik P] or [P Ik], where Ik is the identity matrix of size k.

Data Types: `single` | `double`

Parity-check matrix, specified as a (n-k)-by-n matrix of binary values. The standard form of a parity-check matrix for a [n,k] binary linear block code is [-P' In-k] or [In-k -P'], where In-k is the identity matrix of size (n-k).

Data Types: `single` | `double`

Output Arguments

collapse all

Parity-check matrix, returned as a (n-k)-by-n matrix of binary values corresponding to the generator matrix `G`. The standard form of a parity-check matrix for a [n,k] binary linear block code is [P ' In-k] or [In-k -P '], where In-k is the identity matrix of size (n-k)

Data Types: `single` | `double`

Generator matrix, returned as a k-by-n matrix of binary values corresponding to the parity-check matrix `H`. The standard form of a generator matrix for a [n,k] binary linear block code is [Ik P] or [P Ik], where Ik is the identity matrix of size k.

Data Types: `single` | `double`

collapse all

Generator and Parity-Check matrices

Generator matrices and parity-check matrices are parameters that are required in order to process [n,k] generic linear block codes. For more information, see Configure Parameters for Linear Block Codes.

Version History

Introduced before R2006a