Design a system where constraint length is 5 and code rate is over a binary symmetric channel (BSC) by considering the following conditions.

a) Determine your own specific generator polynomials.

1. Write the connection vectors as vector representation.2. Write the polynomials.

b) Draw the circuit diagram of the register with generator polynomials.

c) Draw the state diagram for the convolutional encoder by creating a table as in Example 7.1. (It is assumed that the initial contents of the register are all zeros.)

d) Determine your own message with 5 words consisting of 1's and 0's. (It is important to know that messages must not be the same for any of the two or more students)

. e) Find the impulse response of the encoder.

f) Using the impulse response, determine the output sequence.

g) Verify the output sequence by using generator polynomials

. h) Draw the tree diagram for the convolutional encoder

. i) Please draw the encoding trellis diagram and show the states and branch words for the convolutional encoder clearly.

j) Configure the cells as implemented in an ACS algorithm.

k) Assign appropriate codewords a, b, c, d, e with random numbers(1's and 0's) and find the decoded symbol using maximum likelihood decoder when the codewords are a, b, c, d, e

. l) Determine your own specific received sequence in 5 words (? bits) with 1 bit error. (Hint: if the transmitted sequence is 10 11 00 01 11, the received sequence can be 10 11 00 01 01 where the red color shows the error in one bit)

m) Using sequential decoding, illustrate the path along the tree diagram.

n) Draw the decoder trellis diagram

. o) Draw the state metrics at each time.

p) Find the maximum likelihood path through the trellis diagram.

q) Find the first 5 bit decoded information bits.

r) Identify any channel bits in Z that were inverted by the channel during transmission.

s) Find the decoded information bits.

t) Change the code rate as and calculate all of the steps from a to s, again.

u) Compare the code rate performance by using the information found.

v) Calculate the error-correcting capability of the code with an example.

w) Compare the Hard and Soft Decision Viterbi Decoding with an example and comment on them. Which one is better? Why?