Let us consider a binary symmetric channel, as shown in Figure 1, where the probability distribution of the input X is given by Pr[X=0] = m and Pr[X = 1] = 1 - m, and the error probability during the transmission is denoted by p. 1-p 0 0 X X р P 1-p Figure 1: A typical binary symmetric channel, where the input is X and the output is Y. р 1 a) Given that p = 1/3 and m = 3/4, compute H(X), H (Y) and H(Y|X). b) Still given p = 1/3. Compute the capacity of this binary symmetric channel. 0 c) Now consider a new binary channel which consists of two original binary symmetric channels con- nected in series as shown in Figure 2. 1-p Y 1 P P 1-p 0 Y 1-p 1-p Figure 2: A new binary channel given by the series connection of two original and identical binary symmetric channels. The parameter p is still the error probability for transmission over one binary symmetric channel. 1 Given that p = 1/3. Compute the capacity of this new binary channel.
Let us consider a binary symmetric channel, as shown in Figure 1, where the probability distribution of the input X is given by Pr[X=0] = m and Pr[X = 1] = 1 - m, and the error probability during the transmission is denoted by p. 1-p 0 0 X X р P 1-p Figure 1: A typical binary symmetric channel, where the input is X and the output is Y. р 1 a) Given that p = 1/3 and m = 3/4, compute H(X), H (Y) and H(Y|X). b) Still given p = 1/3. Compute the capacity of this binary symmetric channel. 0 c) Now consider a new binary channel which consists of two original binary symmetric channels con- nected in series as shown in Figure 2. 1-p Y 1 P P 1-p 0 Y 1-p 1-p Figure 2: A new binary channel given by the series connection of two original and identical binary symmetric channels. The parameter p is still the error probability for transmission over one binary symmetric channel. 1 Given that p = 1/3. Compute the capacity of this new binary channel.
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