2. (a) Explain the principle of Hamming encoder and decoder. [20%] (b) Given that [1 0 1 0 1 0 0] is a (7,4) linear block codeword, complete the following parity check equations. Provide your reasoning. Vi 0 VO 0 ]+0+ V3 = 0 [20%) (C) Given the parity check equations in Q2(b), is [0011011] a codeword? Provide your reasoning. If you think it is not a codeword, indicate which bit is in error. [20%) (d) Is (7,4) Hamming code a perfect code? Provide your reasoning. [15%) (e) A linear block encoder is developed to protect a short message containing 2 information bits. The channel codec is required to be able to correct at most two bits in error. With this requirement, how many parity check bits are needed at the minimum? Provide your reasoning [25%)