Yashpal Singh

The Kraft-McMillan inequality is a foundational result in information theory that establishes a crucial constraint on the lengths of codewords in uniquely decodable codes. Developed independently by Leon Kraft in 1949 and Brockway McMillan in 1956, the inequality is essential for understanding how information can be efficiently encoded while ensuring that no ambiguities arise during … Read more

Prefix codes, also known as prefix-free codes, are a class of uniquely decodable codes where no codeword is a prefix of another. These codes are essential in data compression and communication systems because they enable instantaneous decoding without requiring lookahead or backtracking. Definition and Properties Prefix Codes A prefix code is a set of codewords … Read more

In information theory and coding theory, uniquely decodable codes (UD codes) play a crucial role in ensuring reliable communication. These codes allow the receiver to decode a message sequence uniquely, irrespective of the coding scheme used. The concept of uniquely decodable codes is central to compression and error-free data transmission systems. What Are Uniquely Decodable … Read more

Data compression reduces the size of data for efficient storage and transmission without significant information loss. At its core lies the concept of modeling: representing data in a structured form that facilitates compression. Various mathematical models exploit patterns and redundancies in data, enabling effective compression. Four primary models are Physical Models, Probability Models, Markov Models, … Read more

In the modern digital era, the exponential growth of data has made efficient storage and transmission essential. Lossless compression, a critical technique in data management, achieves this efficiency by reducing file sizes without altering the original content. Unlike lossy compression, which trades accuracy for smaller sizes, lossless compression ensures the exact restoration of the original … Read more