Conditional Probabilities

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Introduction and Background Material
0.1. Message transmission through a noisy communication channel
A digital message “M” is created and sent through a noisy communication channel (Figure 1). The signal “S” to be transmitted consists of a series of zeros and ones:
• symbol “0” appears in the signal with probability 0p
• symbol “1” appears in the signal with probability 101pp=−
The transmitted signal “S” is received at the other end of the channel as signal “R”. Due to noise in the communication channel, a transmitted bit may change during transmission:
• a transmitted bit 0 may be received as 1 with probability 0ε(probability of transmission error for symbol 0);
• a transmitted bit 1 may be received as 0 with probability 1ε(probability of transmission error for symbol 1).
The errors for different symbol transmissions are independent.

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