In your own words, explain the importance of line coder in digital communication. In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a transmission line. Assuming that you are about to send a set of bit string: 1000 1001 1101 0110 down to the transmission line, illustrate the resulted coded signal after it went through line coder using bi-phase M code formats.

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Consider the following linear block code: Each codeword consists of 3 data bits and 3 parity check bits, i.e., [i,,i2,i3,PuP2, P3]- The parity check bits are defined by P1 = i1 + iz P2 = i1 + iz mod 2 P3 = i2 + iz mod 2 mod 2 a. Determine the generator matrix. b. List all the legitimate codewords. c. Determine the minimum distance. d. Suppose that a single error occurs at the first bit. Compute the syndrome. Similarly, compute the syndrome for a single error at each of the other bits. e. Suppose that at most one error occurs. Correct the received vector [010001] by syndrome decoding.