cp5601t2 - d What is the minimum number of bit errors that...

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CP5610 tutorial 2 (from textbook chapter 3) 3.56 Suppose a transmission channel operates at 3 Mbps and that it has a bit error rate of 10 -3 . Bit errors occur at random and independent of each other. Suppose that the following code is used. To transmit a 1, the codeword 111 is sent; To transmit a 0, the codeword 000 is sent. The receiver takes the three received bits and decides which bit was sent by taking the majority vote of the three bits. Find the probability that the receiver makes a decoding error. 3.57 An early code used in radio transmission involved using codewords that consist of binary bits and contain the same number of 1s. Thus, the 2-out-of-5 code only transmits blocks of 5 bits in which 2 bits are 1 and the others 0. a. List the valid codewords. b. Suppose that the code is used to transmit blocks of binary bits. How many bits can be transmitted per codeword? c. What pattern does the receiver check to detect errors?
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Unformatted text preview: d. What is the minimum number of bit errors that cause a detection failure? 3.60 Let g(x)=x 3 +x+1. Consider the information sequence 1001. a. Find the codeword corresponding to the preceding information sequence. b. Suppose that the codeword has a transmission error in the first bit. What does the receiver obtain when it does its error checking? 3.62 Suppose a header consists of four 16-bit words: (11111111 11111111, 11111111 00000000, 11110000 11110000, 11000000 11000000). Find the internet checksum for this code. 3.63 Let g 1 (x) = x + 1 and let g 2 (x) = x 3 + x 2 + 1. Consider the information bits (1,1,0,1,1,0). a. Find the codeword corresponding to these information bits if g 1 (x) is used as the generating polynomial. b. Find the codeword corresponding to these information bits if g 2 (x) is used as the generating polynomial....
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