A coding scheme unlike any Huffman codes — “Intelligence is the ability to adapt to change” — Stephen Hawking (1942–2018) This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Introduction Previous coding schemes that have been covered in this blog have operated under the same principle: The more frequent a symbol is…

How to make a simpler prefix code — “Research is what I’m doing when I don’t know what I’m doing.” — Wernher von Braun This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Introduction If given a string of numbers to compress, it is unlikely that a single compression algorithm will perform…

Real-world examples of Huffman Coding in practice — “My products are my students.” — David Huffman This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Lossless Image Compression A simple task for Huffman coding is to encode images in a lossless manner. This is useful for precise and critical images such as medical images…

Create Huffman codes while reading symbols for the first time — “Science is organized knowledge. Wisdom is organized life.” — Immanuel Kant This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Introduction Previous articles of mine have covered how to create Huffman codes under a variety of different conditions. However, there has always been an…

An efficient coding scheme for integers — “The question of whether anything that was taught or studied in the mathematics department had any practical applications could not even be asked, let alone discussed” — Solomon Golomb This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Introduction The Golomb-Rice coding schemes are…

How to construct Huffman codes with limited computational power and memory — [This method] provides another starting point from which the space-efficiency of the length-limited coding problem can be explored, and may yield algorithms of practical significance. — Moffatt and Katajainen (1995) This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Introduction

How to find an upper-bound for the complexity of data — “The human brain is incapable of creating anything which is really complex” — Andrey Kolmogorov This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Introduction Although scientists and mathematicians have been studying the topic of complexity for hundreds of years, it has yet to…

How to create Huffman codes under a size constraint — “We cannot solve our problems with the same thinking we used when we created them.” — Albert Einstein This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Introduction My previous article, HERE, introduced the fundamentals of Huffman codes and how to create them for…

How to generate optimal codes for any given probability model — “It is the facts that matter, not the proofs. Physics can progress without the proofs, but we can’t go on without the facts.” — Richard Feynman This article is inspired by Introduction to Data Compression 5th edition. Chapter 3 — Sayood, Khalid Introduction In the year 1952, a college student at…