Topic: Communication Systems
The R=1/3 convolution encoder defined by transfer functions $H1(z) = 1 + z^{-1}$, $H2(z) = 1 + z^{-2}$, $H3(z) = 1 + z^{-1} + z^{-2}$ is
- A. Recursive and K = 3
- B. Systematic and K = 2
- C. Non-recursive and K = 3
- D. Non-recursive and K = 2
Answer: C. Non-recursive and K = 3
Explanation: Since all transfer functions are finite polynomials in $z^{-1}$, there is no feedback loop, meaning it is a Non-Recursive encoder. The highest degree of $z^{-1}$ is 2, indicating 2 memory elements ($m=2$). The constraint length $K$ is $m + 1 = 3$.