Data packets containing $100$ bits are transmitted over a communication link. A transmitted bit is received in error $($either a $0$ sent is mistaken for a $1,$ or a $1$ sent is mistaken for a $0$ with probability epsilon $=0\mathrm{.}01,$ independent of the correctness of any other bit. The packet has been coded in such a way that if three or fewer bits are received in error, then those bits can be corrected. If more than three bits are received in error, then the packet is decoded with errors.

Suppose the communication link has different error probabilities for transmitting $0$ and $1.$ When a $1$ is sent, it is received as a $0$ with probability $0\mathrm{.}01.$ when a $0$ is sent, it is received as a $1$ with probability $0\mathrm{.}03.$ Each bit in a packet is still equally likely to be a $0$ or $1.$ Packets have been coded such that if five or fewer bits are received in error, then the packet can be decoded. Simulate the transmission of $300$ packets, each containing $120$ bits. Count the number of packets decoded correctly.

Use MATLAB or any other computer language$/$platform to do the problem. Hand in the following.

a$.$ Identify the language$/$platform you used, and provide a printout of your program$/$script$.$

b$.$ Give the count of the number of correctly decoded packets and the relative frequency of

correctly decoded packets. This relative frequency would be an estimate of the true

probability