Source coding is the process of conversion of the output of the DMS into a sequence of the binary symbol (BCD). It helps in the data compression of naturally redundant messages for efficient storage or transmission.
Shannon Fano Coding:
Symbol probabilities step-1 step-2 step-3 code
Xi P( Xi )
X1 0.5 0 0
X2 0.25 1 0 10
X3 0.125 1 1 0 110
X4 0.125 1 1 1 111
Here,
H(x) =
= – (-0.5-0.5-0.375-0.375)
=1.75
and,
L=
=1*0.5+2*0.25+3*0.125+3*0.125
=1.75
Then,
η(sf) = H(x)/L= 1.75/1.75*100%
η(sf) = 100%……………….(1)
Now, for BCD coding :
in BCD coding length of the codeword is 4 digits
so, L= 4*(0.5+0.25+0.125+0.125)
=4
η(BCD)= H/L*100%
= 1.75/4*100
η(BCD)= 43.75 …………………………(2)
From equation (1) and equation (2), it is clear that the efficiency of Shannon fano coding is greater than that of BCD coding.
2071 Chaitra (Q) Explain the importance of source coding in digital communication systems. A discrete memoryless source emits four symbols with probabilities p= {0.125,0.125,0.25,0.5}. If the output symbols are encoded using Shannon Fano Code, Find the coding Efficiency and Compare the coding efficiency with that of BCD code.
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