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 Matrix	Standard Form	Dimensions
Generator	[I_k P] or [P I_k]	k-by-n
Parity-check	[-P`'` I_n-k] or [I_n-k -P`'` ]	(n-k)-by-n

where I_k 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 Parity-Check Matrix for a Hamming Code to Generator Matrix

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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

Version History

Introduced before R2006a