Assignment #A$6$

Q$1.$ A discrete memoryless source $($DMS$)$ generates three symbols $m_1,m_2,$ and $m_3$ with associated probabilities:

$P(m_1)=0\mathrm{.}5$

$P(m_2)=0\mathrm{.}25$

$P(m_3)=0\mathrm{.}25$

Determine the entropy if the transmitter omits blocks of symbols, where each block consists of two independent symbols that can take any combinations $($a block of two symbols can be: $m_1{m}_1,m_2{m}_1,m_1{m}_2,$ etc.$).$ You need to determine all the possible combinations, determine their corresponding probabilities, and compute the entropy.