# Huffman Code Algorithm Assignment Help Huffman coding is usually a process helpful to compress files with regard to transmission.

Makes use of statistical coding - more frequently utilized symbols have shorter code words.

Works well with regard to text as well as fax transmissions.

An application which utilizes several data structures.

## Huffman coding:

Reducing strings over arbitrary alphabet ‘Σo’ to be able to strings on the ﬁxed alphabet ‘Σc’ to be able to standardize device operations (‘|Σc|<|Σo|’).

Binary representation related to each operands and operators in machine instructions in computers.

It must be feasible so as to uniquely decode the code-string (string over Σc) to a source-string (string over Σo).

Not every code-string has to correspond to a source-string

Both the actual coding as well as decoding ought to become efﬁcient.

Word: A ﬁnite non-empty string over an alphabet (‘Σo or Σc’).

## Simple Coding Mechanism:

• code(ai) = a non-empty string over Σc, for ai∈Σo.
• code(a1a2…an) = code(a1).code(a2)…code(an).

### Example:

Σ0 =(A, B, C, D, E) and Σc =(0, 1)

ABCDEPefix-property
000001010011100Code(AAB)=000.000.001, easy to decodeyes
001001000100001Code(C)=code(AB)=001, not always possible to uniquely decodeno
101001000100001Prefix free codeyes
110100100010000Not prefix free codeno

## Huffman Code Example:

 Symbol A B C D Frequency 13% 25% 50% 12% Original Encoding 00 01 10 11 2 bits 2 bits 2 bits 2 bits Huffman Encoding 110 10 0 111 3 bits 2 bits 1 bit 3 bits

### Expected size:

Original => 1/8x2 + 1/4x2 + 1/2x2 + 1/8x2 = 2 bits / symbol

Huffman => 1/8x3 + 1/4x2 + 1/2x1 + 1/8x3 = 1.75 bits / symbol

### Huffman Coding Example:

 E = 01 I = 00 C = 10 A = 111 H = 110 Huffman code

#### Huffman Coding (coding redundancy): ## The variable-length coding technique:

Symbols tend to be encoded one at a time- (There's a one to one correspondence between source symbols as well as code words)

Optimal code (i.e., minimizes code word length per source symbol).

### Huffman Code Algorithm Overview:

• Encoding.
• Compute frequency associated with symbols in file.
• Generate binary tree which represents best encoding.
• Make use of binary tree in order to encode compressed file- For every symbol, output path through root to leaf as well as Size of encoding = length of path.
• Save binary tree.

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