6.4 Probability and error detection

Let’s return to our repetition code for error detection from section 2.1 0 to a 1 or a 1 to a 0 is p. The probability that no error occurs is 1 - p, as above.

This is called a binary symmetric channel. We have two representations for information, the bits, and hence ‘‘binary.’’ The probability of something bad happening to a 0 or 1 is the same, and that’s the symmetry.

Here is the scheme:

• Create a message to be sent to someone.
• Transform that message by encoding it so that it contains extra information. This will allow it to be repaired if it is damaged en route to the other person.
• Send the message. ‘‘Noise’’ in the transmission may introduced errors in the encoded message.
• Decode the message, using the extra information stored in it to try to fix any transmission errors.
• Give the message to the intended recipient.
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