A description of the Huffman source encoding algorithm.
One particular
source coding algorithm is the Huffman encoding algorithm. It is a source coding
algorithm which approaches, and sometimes achieves, Shannon's bound forsource compression. A brief discussion of the algorithm is also given in
another module .
Huffman encoding algorithm
Sort source outputs in decreasing order of their probabilities
Merge the two least-probable outputs into a single output whose
probability is the sum of the corresponding probabilities.
If the number of remaining outputs is more than 2, then go to
step 1.
Arbitrarily assign 0 and 1 as codewords for the two remaining
outputs.
If an output is the result of the merger of two outputs in a
preceding step, append the current codeword with a 0 and a 1 toobtain the codeword the the preceding outputs and repeat step 5. If
no output is preceded by another output in a preceding step, thenstop.
$\mathrm{Average\; length}=\frac{1}{2}\times 1+\frac{1}{4}\times 2+\frac{1}{8}\times 3+\frac{1}{8}\times 3=\frac{14}{8}$ . As you may recall, the entropy of the source was
also
$H(X)=\frac{14}{8}$ .
In this case, the Huffman code achieves the lower bound of
$\frac{14}{8}\frac{\mathrm{bits}}{\mathrm{output}}$ .
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