Communications Toolbox

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	[Ik P] or [P Ik]	k-by-n
Parity-check	[-P' In-k] or [In-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

The commands below convert the parity-check matrix for a Hamming code into the corresponding generator matrix and back again.

• parmat = hammgen(3)
  genmat = gen2par(parmat)
  parmat2 = gen2par(genmat) % Ans should be the same as parmat above
  

The output is

• parmat =
  
       1     0     0     1     0     1     1
       0     1     0     1     1     1     0
       0     0     1     0     1     1     1
  
  genmat =
  
       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
  
  parmat2 =
  
       1     0     0     1     0     1     1
       0     1     0     1     1     1     0
       0     0     1     0     1     1     1
  

See Also
cyclgen, hammgen

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