Question

The capacity of a discrete lossless channel, with 3 input symbols and 5 output symbols, is ______bits/symbol.

• A. 1.585

Answer 1

The correct option is A 1.585
For a lossless channel,
$H\left(X|Y\right)=0$
$\text{So,}I(X;Y)=H\left(X\right)-H\left(X|Y\right)=H\left(X\right)$
$\text{Channel capacity,}{C}_S=\begin{array}{c}\text{max}\\ \left\{P\right(X\left)\right\}\end{array}I(X;Y)=\begin{array}{c}\text{max}\\ \left\{P\right(X\left)\right\}\end{array}H\left(X\right)={\log }_2\left(m\right)\text{bits/symbol}$
Where, m = number of input symbols.
Given that, m=3.
$\text{So,}{C}_S={\log }_2\left(3\right)=1.585\text{bit/symbol}$