gen2par

Convert between parity-check and generator matrices

Syntax

parmat = gen2par(genmat)
genmat = gen2par(parmat)

Description

parmat = gen2par(genmat) converts the standard-form binary generator matrix genmat into the corresponding parity-check matrix parmat.

genmat = gen2par(parmat) converts the standard-form binary parity-check matrix parmat into the corresponding generator matrix genmat.

The standard forms of the generator and parity-check matrices for an [n,k] binary linear block code are shown in the table below

Type of MatrixStandard FormDimensions
Generator [Ik P] or [P Ik] k-by-n
Parity-check [-P' In-k] or [In-k -P' ] (n-k)-by-n

.

where Ik is the identity matrix of size k and the ' symbol indicates matrix transpose. Two standard forms are listed for each type, because different authors use different conventions. For binary codes, the minus signs in the parity-check form listed above are irrelevant; that is, -1 = 1 in the binary field.

Examples

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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