Editing Shannon–Fano coding (section)

===Example with Huffman coding===
[[File:HuffmanCodeAlg.png|right|thumb|300px|Huffman Algorithm]]

We use the same frequencies as for the Shannon–Fano example above, viz:

:{| class="wikitable" style="text-align: center;"
! Symbol
! A
! B
! C
! D
! E
|-
! Count
| 15
| 7
| 6
| 6
| 5
|-
! Probabilities
| 0.385
| 0.179
| 0.154
| 0.154
| 0.128
|}

In this case D & E have the lowest frequencies and so are allocated 0 and 1 respectively and grouped together with a combined probability of 0.282.  The lowest pair now are B and C so they're allocated 0 and 1 and grouped together with a combined probability of 0.333.  This leaves BC and DE now with the lowest probabilities so 0 and 1 are prepended to their codes and they are combined.  This then leaves just A and BCDE, which have 0 and 1 prepended respectively and are then combined.  This leaves us with a single node and our algorithm is complete.

The code lengths for the different characters this time are 1 bit for A and 3 bits for all other characters.

:{| class="wikitable"
! Symbol
! A 
! B 
! C 
! D 
! E
|- 
! Codewords
| 0
| 100 
| 101 
| 110 
| 111
|}

This results in the lengths of 1 bit for A and per 3 bits for B, C, D and E, giving an average length of

:<math display="block">\frac{1\,\text{bit}\cdot 15 + 3\,\text{bits} \cdot (7+6+6+5)}{39\, \text{symbols}} \approx 2.23\,\text{bits per symbol.}</math>

We see that the Huffman code has outperformed both types of Shannon–Fano code, which had expected lengths of 2.62 and 2.28.