Main Content

decode

Block decoder

collapse all in page

Syntax

msg = decode(code,n,k)
msg = decode(code,n,k,codingMethod,prim_poly)
msg = decode(code,n,k,codingMethod,genmat)
msg = decode(code,n,k,codingMethod,genmat,trt)
msg = decode(code,n,k,codingMethod,genpoly)
msg = decode(code,n,k,codingMethod,genpoly,trt)
[msg,err,ccode,cerr] = decode(___)

Description

msg = decode(code,n,k) decodes the coded message code. The function assumes that the Hamming encoding method was used, with codeword length n and message length k.

example

msg = decode(code,n,k,codingMethod,prim_poly) decodes code assuming that prim_poly is the primitive polynomial used for encoding. This syntax applies when codingMethod is 'hamming/binary' or 'hamming/decimal'.

example

msg = decode(code,n,k,codingMethod,genmat) decodes code assuming that genmat is the generator matrix used for encoding. This syntax applies when codingMethod is 'linear/binary' or 'linear/decimal'.

example

msg = decode(code,n,k,codingMethod,genmat,trt) additionally specifies the decoding table trt. This syntax applies when codingMethod is 'linear/binary' or 'linear/decimal'.

msg = decode(code,n,k,codingMethod,genpoly) decodes code assuming that genpoly is the generator polynomial used for encoding. This syntax applies when codingMethod is 'cyclic/binary' or 'cyclic/decimal'.

example

msg = decode(code,n,k,codingMethod,genpoly,trt) additionally specifies the decoding table trt. This syntax applies when codingMethod is 'cyclic/binary' or 'cyclic/decimal'.

[msg,err,ccode,cerr] = decode(___) additionally returns the message word errors err, the corrected codeword ccode, and the codeword errors cerr, using any input argument combination from the previous syntaxes.

Examples

collapse all

Open Live Script

Set the values of the codeword length and message length.

n = 15; % Codeword length
k = 11; % Message length

Create a random binary message with the length equal to the message length.

data = randi([0 1],k,1);

Encode the message.

encData = encode(data,n,k,'hamming/binary');

Corrupt the encoded message by introducing an error at a random location.

errLoc = randerr(1,n);
encData = mod(encData + errLoc',2);

Decode the corrupted sequence. Observe that the decoder has correctly recovered the message.

decData = decode(encData,n,k,'hamming/binary');
numerr = biterr(data,decData)
numerr = 
0
Open Live Script

Set the values of the codeword length and message length.

n = 7; % Codeword length
k = 3; % Message length

Create a random binary message with the length equal to the message length.

data = randi([0 1],k,1);

Create a cyclic generator polynomial. Then, create a parity-check matrix and convert it into a generator matrix.

pol = cyclpoly(n,k);
parmat = cyclgen(n,pol);
genmat = gen2par(parmat);

Encode the message sequence by using the generator matrix.

encData = encode(data,n,k,'linear/binary',genmat);

Corrupt the encoded message by introducing an error at a random location.

errLoc = randerr(1,n);
encData = mod(encData + errLoc',2);

Decode the corrupted sequence. Observe that the decoder has correctly recovered the message.

decData = decode(encData,n,k,'linear/binary',genmat);
Single-error patterns loaded in decoding table.  8 rows remaining.
2-error patterns loaded.  1 rows remaining.
3-error patterns loaded.  0 rows remaining.

numerr = biterr(data,decData)
numerr = 
0
Open Live Script

Set the values of the codeword length and message length.

n = 15; % Codeword length
k = 5; % Message length

Create a random binary message with the length equal to the message length.

data = randi([0 1],k,1);

Create a generator polynomial for a cyclic code. Create a parity-check matrix by using the generator polynomial.

genpoly = cyclpoly(n,k);
parmat = cyclgen(n,genpoly);

Create a syndrome decoding table by using the parity-check matrix.

trt = syndtable(parmat);
Single-error patterns loaded in decoding table.  1008 rows remaining.
2-error patterns loaded.  918 rows remaining.
3-error patterns loaded.  648 rows remaining.
4-error patterns loaded.  243 rows remaining.
5-error patterns loaded.  0 rows remaining.

Encode the data by using the generator polynomial.

encData = encode(data,n,k,'cyclic/binary',genpoly);

Corrupt the encoded message by introducing three errors at random locations.

errLoc = randerr(1,n,3);
encData = mod(encData + errLoc',2);

Decode the corrupted sequence. Observe that the decoder has correctly recovered the message.

decData = decode(encData,n,k,'cyclic/binary',genpoly,trt);
numerr = biterr(data,decData)
numerr = 
0

Input Arguments

collapse all

Input code, specified as one of these options:

  • Binary column or row vector

  • Binary matrix with n columns

  • Column or row vector of integers in the range [0, 2n–1]

Data Types: single | double

Codeword length, specified as a positive integer. The function calculates this value as 2m–1, where m is an integer greater than or equal to 2.

Message length, specified as a positive integer. The function calculates this value as n–m, where m must be greater than or equal to 2.

Error coding method and format, specified as one of these options:

  • 'hamming/binary'

  • 'hamming/decimal'

  • 'linear/binary'

  • 'linear/decimal'

  • 'cyclic/binary'

  • 'cyclic/decimal'

The value you choose for this input determines the syntax you must use. This table summarizes the dependency. The table does not cover the first syntax because you do not specify a value for codingMethod when you use it.

Value of codingMethodSyntax to Use
'hamming/binary' or 'hamming/decimal'2 or 7
'linear/binary' or 'linear/decimal'3, 4, or 7
'cyclic/binary' or 'cyclic/decimal'5, 6, or 7

Data Types: char | string

Primitive polynomial, specified as one of these options:

  • Binary row vector — This vector gives coefficients of prim_poly in the order of ascending powers.

  • Character vector or a string scalar — This value defines prim_poly in textual representation. For more information, see Representation of Polynomials in Communications Toolbox.

  • Positive integer — This value defines prim_poly in the range [2m + 1, 2m + 1 – 1].

For more information, see Default Primitive Polynomials and Primitive Polynomials and Element Representations.

Dependencies

This argument applies when you set CodingMethod to 'hamming/binary' or 'hamming/decimal'.

Data Types: double | char | string

Generator matrix, specified as a k-by-n numeric matrix.

Dependencies

This argument applies when you set CodingMethod to 'linear/binary' or 'linear/decimal'.

Data Types: double

Generator polynomial, specified as a polynomial character vector or a row vector that gives the coefficients in order of ascending powers of the binary generator polynomial. The value of genpoly for an [n, k] cyclic code must have degree n–k and divide xn–1, where x is an identifier.

Dependencies

This argument applies when you set CodingMethod to 'cyclic/binary' or 'cyclic/decimal'.

Data Types: double | char | string

Decoding table, specified as a 2n-k-by-n binary matrix. Create the decoding table using the syndtable function.

Dependencies

This argument applies when you set CodingMethod to 'linear/binary', 'linear/decimal', 'cyclic/binary', or 'cyclic/decimal'.

Output Arguments

collapse all

Decoded messages, returned as one of the options in the table. The value and dimension of msg depends on the value and dimension of code and the input message format.

code ValueInput Message Formatmsg Value

binary column or row vector

binary

binary column or row vector

binary matrix with n columns

binary

binary matrix with k columns

column or row vector of integers in the range [0, 2n–1]

decimal

column or row vector of integers in the range [0, 2k–1]

Data Types: single | double

Message error correction information, returned as a column vector of integers. The length of the vector is equal to the number of message words. The vector entries can take these values:

  • 0 — The function did not detect an error in the corresponding message word.

  • 1 — The function detected and corrected an error in the corresponding message word.

  • –1 — The decoding algorithm detected more errors in the corresponding message word than could be corrected.

Corrected code, returned as one of these options:

  • Binary column or row vector with n columns

  • Binary matrix with n columns

  • Column or row vector with n entries which are integers in the range [0, 2n–1]

The format of ccode matches that of code.

Codeword error correction information, returned as a column vector of integers. The length of the vector is equal to the number of message words. The meaning of this output depends on the format of code. If code is not a binary vector, cerr is equal to err. If code is a binary vector, this output contains error detection information for codewords. The information is given in the same way as in err.

Algorithms

Depending on the decoding method, decode relies on lower-level functions such as hammgen, syndtable, and cyclgen.

Version History

Introduced before R2006a

See Also

| | |

Topics