A communications system uses single parity check codes with soft decision on an AWGN channel with SNR=6.8 dB. Assume that a logical O is mapped to -1.0 V and a logical 1 to +1.0 v. (a) Using the multiplicity and minimum Euclidean distance bound, determine the probability of error for a (4,3) single parity check on this channel. [5 marks) (b) For the (4,3) single parity check code, decode the following received vector: +1.9, +1.2, +0.2,-0.7 using soft decision 0 Bit flipping decoding. [4 marks] (1) Trellis based Viterbi decoding. [4 marks) (ii) Codeword enumeration decoding. [4 marks] (c) Briefly discuss and compare the three decoding methods in Part (b) and indicate which method is optimal for the AWGN channel. [4 marks] (d) Determine the highest data rate for a target probability of error of 0.01 obtainable with single parity check codes on the given channel. [4 marks)