Skip to content Skip to navigation Skip to collection information

OpenStax-CNX

You are here: Home » Content » Principles of Digital Communications » Huffman Coding

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice Digital Scholarship

    This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Digital Communication Systems"

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

Recently Viewed

This feature requires Javascript to be enabled.
 

Huffman Coding

Module by: Behnaam Aazhang. E-mail the author

Summary: 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 for source compression. A brief discussion of the algorithm is also given in another module.

Huffman encoding algorithm

  1. Sort source outputs in decreasing order of their probabilities
  2. Merge the two least-probable outputs into a single output whose probability is the sum of the corresponding probabilities.
  3. If the number of remaining outputs is more than 2, then go to step 1.
  4. Arbitrarily assign 0 and 1 as codewords for the two remaining outputs.
  5. 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 to obtain the codeword the the preceding outputs and repeat step 5. If no output is preceded by another output in a preceding step, then stop.

Example 1

XABCD X A B C D with probabilities { 12 1 2 , 14 1 4 , 18 1 8 , 18 1 8 }

Figure 1
Figure 1 (Figure7-24.png)

Average length=121+142+183+183=148 Average length 1 2 1 1 4 2 1 8 3 1 8 3 14 8 . As you may recall, the entropy of the source was also HX=148 H X 14 8 . In this case, the Huffman code achieves the lower bound of 148bitsoutput 14 8 bits output .

In general, we can define average code length as

-=x X ¯ p X xx x x X ¯ p X x x
(1)
where X ¯ X ¯ is the set of possible values of xx.

It is not very hard to show that

HX->HX+1 H X H X 1
(2)
For compressing single source output at a time, Huffman codes provide nearly optimum code lengths.

The drawbacks of Huffman coding

  1. Codes are variable length.
  2. The algorithm requires the knowledge of the probabilities, p X x p X x for all x X ¯ x X ¯ .
Another powerful source coder that does not have the above shortcomings is Lempel and Ziv.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks