Question

Consider a DMS where output is generated from an alphabet {a,b,c,d,e,f,g,h} with respective with probabilities {0.25, 0.1, 0.02, 0.05, 0.25, 0.03, 0.25, 0.05}.

a) Design a Huffman code and sketch the corresponding coding tree. Explain the codewords for each character in the alphabet

Answer 1

Huffman coding is a lossless data compression technique that assigns variable-length codes to different characters based on their frequencies. The Huffman codes for the given alphabet are: a-11, b-010, c-0010, d-0011, e-10, f-000, g-11, h-001.

Step-by-step explanation:

Huffman coding is a lossless data compression technique commonly used in computer science. It assigns variable-length codes to different characters in a given alphabet based on their frequencies. The most frequent characters are assigned shorter codes, while the less frequent characters are assigned longer codes. This ensures that the most common characters require fewer bits, resulting in more efficient compression.

To design a Huffman code for the given alphabet {a,b,c,d,e,f,g,h}, we first calculate the frequency of each character. Then, we create a binary tree called a coding tree, where each leaf node represents a character, and the path from the root to each leaf node represents the corresponding binary code. The Huffman codes for the given alphabet are as follows:

CharacterHuffman Codea11b010c0010d0011e10f000g11h001

The coding tree is a binary tree, where each internal node has two children representing 0 and 1, respectively. The leaf nodes represent the characters, and their corresponding Huffman codes can be obtained by tracing the path from the root to each leaf node.