A memoryless source emits six messages with probabilities $0\mathrm{.}3,0\mathrm{.}25,0\mathrm{.}15,0\mathrm{.}12,0\mathrm{.}1,$ and $0\mathrm{.}08.$

Find the $4-$ary $($quaternary$)$ Huffman code. Determine its average word length, the efficiency,

and the redundancy.

In this case, we need to add one dummy message to satisfy the required condition of IADLE $14\mathrm{.}0$

The redundancy $=1-=0\mathrm{.}07.$

$r+k(r-1)$ messages and proceed as usual. The Huffman code is found in Table $14\mathrm{.}3.$

The length $L$ of this code is

$L=0\mathrm{.}3(1)+0\mathrm{.}25(1)+0\mathrm{.}15(1)+0\mathrm{.}12(2)+0\mathrm{.}1(2)+0\mathrm{.}08(2)+0(2)$

$=1\mathrm{.}3-$ary digits IADLE $14\mathrm{.}0$

The redundancy $=1-=0\mathrm{.}07.$A memoryless source emits six messages with probabilities $0\mathrm{.}3,0\mathrm{.}25,0\mathrm{.}15,0\mathrm{.}12,0\mathrm{.}1,$ and $0\mathrm{.}08.$

Find the $4-$ary $($quaternary$)$ Huffman code. Determine its average word length, the efficiency,

and the redundancy.

In this case, we need to add one dummy message to satisfy the required condition of

$r+k(r-1)$ messages and proceed as usual. The Huffman code is found in Table $14\mathrm{.}3.$

The length $L$ of this code is

$L=0\mathrm{.}3(1)+0\mathrm{.}25(1)+0\mathrm{.}15(1)+0\mathrm{.}12(2)+0\mathrm{.}1(2)+0\mathrm{.}08(2)+0(2)$

$=1\mathrm{.}3-$ary digits