homework EE

Consider a (𝑛, 𝑘, 𝑚) nonsystematic convolutional code (NSC) with code rate 𝑟 = 𝑘 𝑛⁄ = 1 2⁄ , in which

Generator sequence: 𝑔. = [1 0 1 1], 𝑔2 = [1 1 0 1]

Compact form: 𝐺. = [𝑔., 𝑔2] (1) Convert it into a RSC encoder: 𝐺2 = [1, 𝑔2/𝑔.]

(2) What is the constraint length of the code?

(3) Draw a hardware realization of the RSC encoder.

(4) Determine the state table of the RSC encoder

(5) Draw the state diagram of the RSC encoder

Label the branches of the state diagram with input/output values.

(6) Incorporate 𝐺2 in the following turbo encoder with interleaver

п = {5, 4, 8, 1, 9, 7, 3, 0, 2, 6}

For the input sequence 𝑚 = (1,1,0,1,0,0,1,1,0,1), assume the encoder starts from state 0.

(7) Find the codeword bit stream 𝒗 if the encoded bits are not punctured.

(8) Find the codeword bit stream 𝒗 if the encoded bits are punctured with 𝑃 = A0 1 1 0

B.