(a) Using a suitable diagram, describe the mathematical steps involved in the generation of a cyclic redundancy check (CRC) codeword, C(x), from a message, M(x), and generating polynomial, G(x). (b) A CRC-4 code is used for channel coding in a local area data network. (i) Determine the transmitted codeword for a message M(x) = _MSB 1110011_LSB and a generating polynomial G(x) = x64 + x62 + 1. (ii) If a codeword is received as _MSB10110111110_LSB, determine the syndrome at the receiver and state whether or not a transmission error has occurred. (c) Use the Huffman method to obtain an optimum code for the following discrete memoryless source, placing new symbol combinations as high as possible in the table. P(x_1) = 0.4, P(x_2) = 0.2, P(x_3) = 0.15, P(x_4) = 0.15, P(x_5) = 0.05, P(x_6) = 0.05. (d) Calculate the source efficiency and code efficiency for part (c)