A $(7,4)$ cyclic codes has a generator polynomial: $g(X)=X^{3}+X+1$ (a) Draw the block diagram of encoder and syndrome calculator
Explanation
The problem requires us to draw the block diagram of the encoder and syndrome calculator for a (7,4) cyclic code with generator polynomial g(X) = X^3 + X + 1. The encoder can be implemented using a shift register, and the syndrome calculator can be implemented using a series of modulo-2 adders and a shift register. The block diagram of the encoder and syndrome calculator is as follows.
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