Understanding the Huffman coding procedures in digital communication with examples

The information theory is related to the concepts of statistical properties of messages / sources, channels, noise interference etc. The information theory is used for mathematical modeling and analysis of the communication systems, following two main points are resolved:

1). The irreducible complexity below which the signal can not be compressed.

2). The transmission rate for reliable communication over a noisy channel.

Huffman coding also uses the same principle. This type of coding makes average number of binary digits per message nearly equal to Entropy ( average bits of information per message). This is a variable length and prefix free coding. So there is different length code words and no code words are prefix of others. It gives the advantages of variable length and prefix free coding like - required less bandwidth.

Huffman coding is a widely used algorithm for lossless data compression in digital communication. It works by assigning shorter binary codes to frequently occurring symbols and longer binary codes to less frequently occurring symbols. This results in a more efficient representation of the data, as the more common symbols can be represented with fewer bits than the less common symbols.

The algorithm begins by analyzing the input data and creating a frequency table that shows the number of occurrences of each symbol. The symbols are then arranged in order of decreasing frequency, and a binary tree is constructed by repeatedly merging the two least frequent symbols until all symbols are accounted for. The binary codes are assigned by traversing the tree from the root to each symbol, with a "0" assigned for each left branch and a "1" assigned for each right branch.

The resulting Huffman code is optimal in the sense that it produces the smallest possible number of bits needed to represent the input data. This makes it a popular choice for compressing data in digital communication systems, where efficient use of bandwidth and storage space is critical.

Huffman coding can be best explained with the help of an example, which can be presented in two ways: through text images or a video. If you prefer to read, then you can follow the text images, but if you would rather watch, then you can view the following video: 

Table: 1.8.3

Table: 1.8.4

You can also practice following examples. I collect all these examples and their coding methods to enhance your practical knowledge.

Example-1

Example-2

Example-3