Binary Linear Decoder

Decode linear block code to recover binary vector data

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Libraries:
Communications Toolbox / Error Detection and Correction / Block

Description

The Binary Linear Decoder block recovers a binary message vector from a binary codeword vector of a linear block code. For more information, see Linear Block Coding.

For proper decoding, the parameter values in this block must match those in the corresponding Binary Linear Encoder block.

Examples

Create Binary Linear Code in Binary Format Using Simulink

This example shows how to model a simple encoder and decoder using appropriate vector lengths for the code and message.

The cm_binary_linear model includes these blocks:

• Bernoulli Binary Generator block with Samples per frame set to 4 to match the binary linear encoder message length

• Binary Linear Encoder block with default parameter values

• Binary Linear Decoder block with default parameter values

• Error Rate Calculation block with Output data set to Port

• Display block connected to the output port of the Error Rate Calculation block

To display the vector length of signals in the model, go to Debug > Diagnostics > Information Overlays > Signals and select Signal Dimensions. The connector lines show the signal attributes. To compile the model, press Ctrl+D. Run the model to display the error rate statistics.

Ports

Input

In — Encoded message

binary column vector

Encoded message, specified as a binary column vector containing N elements. N equals the number of columns in the generator matrix specified by the Generator matrix (binary K-by-N matrix) parameter. This port is unnamed on the block mask.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point | enumerated | bus
Complex Number Support: Yes

Output

Out — Decoded message

column vector

Decoded message, returned as a column vector output signal containing K elements and having the same data type as the input port, In. K must equal the number of rows in the generator matrix specified by the Generator matrix (binary K-by-N matrix) parameter. This port is unnamed on the block mask.

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Generator matrix (binary K-by-N matrix) — Generator matrix

[[1 1 0; 0 1 1; 1 1 1; 1 0 1] eye(4)] (default)

Generator matrix for the code, specified as a K-by-N matrix, where K is the message length and N is the codeword length. For more information, see Linear Block Coding.

Decoding table (0 for table corresponding to Generator matrix) — Decoding table

0 (default) | matrix

Decoding table, specified as 0 or a 2^(N–K)-by-N matrix that lists correction vectors for each codeword's syndrome.

• When this parameter is zero (0), the block uses the output of syndtable(H) as the decoding table for the code. The input, H, is an (N–K)-by-N parity-check matrix for the code.

• When this parameter is a matrix, the matrix must be a 2^(N–K)-by-N binary matrix. For more information, see Decoding Table.

Block Characteristics

Data Types	Boolean | double | fixed point | integer | single
Multidimensional Signals	no
Variable-Size Signals	no

More About

Linear Block Coding

The process of encoding a message into an [N,K] linear block code is determined by a K-by-N generator matrix G.

Specifically, a 1-by-K message vector v is encoded into the 1-by-N codeword vector vG. If G has the form [I_k, P] or [P, I_k], where P is some K-by-(N–K) matrix and I_k is the K-by-K identity matrix, G is said to be in standard form.

This block expects the Generator matrix (binary K-by-N matrix) parameter to be in standard form, as defined in [1].

Decoding Table

The decoding table is a 2^(N–K)-by-N binary matrix. K is the message length and N is the codeword length.

The decoder attempts to correct errors, using the decoding table. The decoding table tells the decoder how to correct errors that may have corrupted the code during transmission. The rth row of this matrix is the correction vector for a received binary codeword whose syndrome has decimal integer value r–1. The syndrome of a received codeword is its product with the transpose of the parity-check matrix.

References

[1] Clark, George C., and J. Bibb Cain. Error-Correction Coding for Digital Communications. Applications of Communications Theory. New York: Plenum Press, 1981.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a