Shannon-Fano Algorithm for Data Compression

Introduction

Effective data compression is essential for lowering storage needs and bandwidth usage in the field of data processing & transmission. To achieve this, numerous algorithms have been created; the Shannon-Fano algorithm was among the first to be created. This algorithm, which was made during the 1940s by Robert Fano and Claude Shannon, was set up for later improvements in data compression techniques. The method of shrinking a data record to such an extent that it occupies less disk space or requires less resources to send is known as data compression.

It tends to be generally partitioned into two classes: lossy compression, in which some data is lost during compression, and lossless compression, in which the original data can be perfectly reproduced from the compressed data. Since the Shannon-Fano technique is a lossless compression methodology, it is utilized in circumstances where it is vital to keep up with the entirety of the data.

An Understanding of the Algorithm Shannon-Fano

The Shannon-Fano algorithm functions by analyzing how frequently certain symbols appear in the input data. It uses a systematic process to compress data by giving more often occurring symbols shorter codewords. This is the algorithm broken down step-by-step:

1. Frequency Analysis: To ascertain the frequency of occurrence of every character or letter, the algorithm first analyses the input data. This entails keeping track of how many times each symbol appears in the data.
2. Symbol Sorting: After the frequencies of the symbols are ascertained, they are arranged according to their frequencies in a non-increasing order. When sorting, characters with higher frequencies are prioritized.
3. Partitioning: Following sorting, the characters are divided into two sets so that each set's total frequencies are roughly equal. Recursive partitioning is carried out until each set has just one symbol.
4. Codeword Assignment: Following the partitioning process, codewords are subsequently allocated to every symbol. It is common practice to assign '0' to symbols located in the first partition and '1' to symbols located in the second partition. Until a binary codeword uniquely identifies every symbol, this assignment is carried out recursively.
5. Compression:Lastly, a compressed version of the original information is produced by encoding the input data using the designated codewords.

Shannon-Fano Compression Example

Let's look at a little example to demonstrate the Shannon-Fano algorithm. Take a look at the incoming data below:

Input Data: "ABBCCCDDDDEEEEE"

Step 1: Analysis of Frequency

Symbol frequency:

A: 1

B: 2

C: 3

D: 4

E: 5

Step 2: Sorting Symbols

Put symbols in order of frequency:

E, D, C, B, A

Step 3: Partitioning

Divide the characters into two groups that have roughly equal frequencies:

Set 1: E, D (frequency: 9)

Set 2: C, B, A (frequency: 6)

Step 4: Assigning Codewords

Put '0' to Set 1 symbols and '1' to Set 2 symbols.

Set 2:

D: 0

E: 0

C: 10

B: 11

A: 12

Step 5: Compression

Utilizing the supplied codewords, encrypt the input data:

"001110111112222222222" is the compressed data.

Code

Output:

Code Explanation

• To hold symbol-frequency pairs & symbol-code pairs, respectively, two structures are defined: SymbolFreq and SymbolCode.
• The symbol-frequency pairings are sorted in descending order by the sort function based on frequency.
• The Shannon-Fano algorithm is used iteratively by the shannon_fano function to assign codes to symbols.
• The user enters a string in the main function.
• Each character in the string has its frequency counted and saved in a frequency array.
• To sort the symbols according to their frequencies, the sort function is called.
• Symbol codes are assigned by calling the shannon_fano function.
• The sorted symbols are printed with their codes and frequency.

Conclusion

The Shannon-Fano algorithm offers a fundamental comprehension of strategies for data compression. The Shannon-Fano method, which prioritizes symbols according to their frequencies, continues to be a fundamental component in the development of data compression.