# Binary Linear Decoder

Decode linear block code to recover binary vector data

## Library

Block sublibrary of Error Detection and Correction

## Description

The Binary Linear Decoder block recovers a binary message vector from a binary codeword vector of a linear block code.

The Generator matrix parameter is the generator matrix for the block code. For proper decoding, this should match the Generator matrix parameter in the corresponding Binary Linear Encoder block. If N is the codeword length of the code, then Generator matrix must have N columns. If K is the message length of the code, then the Generator matrix parameter must have K rows.

This block accepts a column vector input signal containing N elements. This block outputs a column vector with a length of K elements.

The decoder tries to correct errors, using the Decoding table parameter. If Decoding table is the scalar 0, then the block defaults to the table produced by the Communications Toolbox™ function syndtable. Otherwise, Decoding table must be a 2N-K-by-N binary matrix. 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.

For information about the data types each block port supports, see the Supported Data Type table on this page.

## Parameters

Generator matrix

Generator matrix for the code; same as in Binary Linear Encoder block.

Decoding table

Either a 2N-K-by-N matrix that lists correction vectors for each codeword's syndrome; or the scalar 0, in which case the block defaults to the table corresponding to the Generator matrix parameter.

## Supported Data Type

PortSupported Data Types
In
• Double-precision floating point

• Single-precision floating point

• Boolean

• 8-, 16-, and 32-bit signed integers

• 8-, 16-, and 32-bit unsigned integers

• Fixed-point

Out
• Double-precision floating point

• Single-precision floating point

• Boolean

• 8-, 16-, and 32-bit signed integers

• 8-, 16-, and 32-bit unsigned integers

• Fixed-point

## Pair Block

Binary Linear Encoder

## Version History

Introduced before R2006a