Plot the probability of error for hard decision decoding

Question

Response to the following problem:

The rate 1/3, K = 3, binary convolutional code with transfer function given by Equation is used for transmitting data over a Rayleigh fading channel via binary PSK.

1. Determine and plot the probability of error for hard decision decoding. Assume that the transmitted waveforms corresponding to the coded bits fade independently.

2. Determine and plot the probability of error for soft decision decoding. Assume that the waveforms corresponding to the coded bits fade independently.

Equation=

T(Y,Z,J) = J³YZ⁶/1 - JYZ²(1 + J)
           =J³YZ⁶ + J⁴Y²Z⁸ + J⁵Y²Z⁸ + J⁵Y³Z¹⁰
              + 2 J⁶Y³Z¹⁰ + J⁷Y³Z¹⁰ + .....