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# Hamming Decoder

Decode Hamming code to recover binary vector data

## Library

Block sublibrary of Error Detection and Correction

## Description

The Hamming Decoder block recovers a binary message vector from a binary Hamming codeword vector. For proper decoding, the parameter values in this block should match those in the corresponding Hamming Encoder block.

If the Hamming code has message length K and codeword length N, then N must have the form 2M-1 for some integer M greater than or equal to 3. Also, K must equal N-M.

This block accepts a column vector input signal of length N. The output signal is a column vector of length K.

The coding scheme uses elements of the finite field GF(2M). You can either specify the primitive polynomial that the algorithm should use, or you can rely on the default setting:

• To use the default primitive polynomial, simply enter N and K as the first and second dialog parameters, respectively. The algorithm uses gfprimdf(M) as the primitive polynomial for GF(2M).

• To specify the primitive polynomial, enter N as the first parameter and a binary vector as the second parameter. The vector represents the primitive polynomial by listing its coefficients in order of ascending exponents. You can create primitive polynomials using the Communications System Toolbox™ gfprimfd function.

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

## Dialog Box

Codeword length N

The codeword length N, which is also the input vector length.

Message length K, or M-degree primitive polynomial

Either the message length, which is also the output vector length; or a binary vector that represents a primitive polynomial for GF(2M).

## 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

Hamming Encoder

## See Also

hammgen (Communications System Toolbox)

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