Information Theory and Coding > Error Control Coding > Encoding the cyclic Code: Non-Systematic Encoding

Encoding the cyclic Code: Non-Systematic Encoding

The generator polynomial function is

Let the message is m = (m₀, m₁,…. m_k-1) then message polynomial is

m(x) = m₀ + m₁x + m₁x² +… + m_k-2 x^k-2 + m_k-1 x^k-1

The codeword polynomial is

C(x) = m(x) g(x)

Example: If m = (1010) and  find the (7,4) codewords.

So codeword will be the coefficients of resultant codeword polynomial (1 1 1 0010)

From the codeword bits, it can clearly interpret that the encoded codeword contains the message and parity bits in an intermixed pattern. Thus, using a non-systematic codeword and direct determination of message bits is not possible.

Prev

What is Cyclic Code?

Next

Encoding and decoding the cyclic Code: Non-Systematic Encoding

Feedback

Submit