In many cases in networks, instead of using all 8 bits for data, we often utilize only 7 bits for data and one bit for 'control'. Specifically, this control bit is an even-parity bit to ensure that the number of bit '1' in total 8 bits-long data is always even.

Assume a binary symmetric channel with bit error probability p _e as in the lecture note. All bit errors are independent of another.

Sender A now transmits an 8-bit long packet (7 data bits + one even-parity bit) onto this binary symmetric channel. The receiver B receives a packet and there are total three possibilities:

• Case 1: no bit has been inverted (no error) so the receiver successfully receives the packet.
• Case 2: Some bits are inverted (error!) and the receiver can correctly 'detect' the error.
• Case 3: Some bits are inverted (error!) but the receiver mistakenly concludes that the packet is (or appears to be) error-free.

Find the probability of each of these three cases. No need to find a closed form. Just leave your expression as is.

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No bit is inverted 1 case only Some bits are inverted a... View the full answer