Consider a communication channel as shown in Figure 9.2. We can model the communication over this channel as follows. At time n, a random variable X_n is generated and is transmitted over the channel. However, the channel is noisy. Thus, at the receiver, a noisy version of Xn is received. More specifically, the received signal is Y_n = X_n +W_n, where W_n ∼ N(0,σ²) is the noise added to X_n. We assume that the receiver knows the distribution of X_n. The goal here is to recover (estimate) the value of X_n based on the observed value of Y_n.

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X₂² Transmitted Signal I Noise: WN(0,0²) Yn = Xn + Wn Received Signal Communication Channel Figure 9.2 - Noisy communication channel in Example 9.2