Question

A simplest error-correcting code would be to transmit every packet three
times on a bit-by-bit basis, which is called repetition code. For example, if a packet
of two data bits is ‘01’, then by the repetition code the actual bits transmitted will be
‘000111’. Receiver receives three values for each data bit (0 or 1) and use a majority
vote as a decoding method for the data bit. If there are two or three 1’s out of the three
values, then the receiver decodes the bit as 1. Similarly for 0. Assume a binary symmetric
channel in which the probability of bit error is pe, independent of all other bits.

(a) What is the probability that a packet of N bits is received incorrectly when the
packet is transmitted only once (i.e., without using the above repetition code)? Find
the expression for the probability in terms of pe. Note that a packet is transmitted
correctly if and only if every bit of the packet is transmitted without error.

(b) What is the probability that a packet of N bits is received incorrectly with using the
repetition code? Find the expression for the probability in terms of pe. Hint: First
find the probability that a given bit (or a packet of 1 bit) is received incorrectly with
using the repetition code.

Answer 1

What do you wanna know ???