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
Data compression plays a vital role in managing the vast amounts of digital information generated daily. It enables the efficient storage, transmission, and retrieval of data by reducing its size while preserving essential content. Two critical components of data compression are modeling and coding. Together, they form the backbone of techniques that make modern communication … Read more
Compression techniques are vital in reducing data size for efficient storage, transmission, and processing. They allow us to store more data in limited space, minimize bandwidth usage, and improve data processing speeds. This article will cover the fundamentals of compression, including various mathematical concepts and algorithms, along with examples and Python code for each. Additionally, … Read more
