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Lecture

Data Compression and Entropy: Conclusion

In course

CS-119(d): Information, Computation, Communication

L'objectif de ce cours est d'introduire les étudiants à la pensée algorithmique, de les familiariser avec les fondamentaux de l'Informatique et de développer une première compétence en programmation (langage C++). ...

Description

This lecture concludes with fundamental concepts to remember, such as the definition of entropy, which measures the amount of information or surprises in a message. It explains entropy as the average number of binary questions needed to find a solution, and delves into the mathematical definition of entropy as the sum of Pi log of 1 over Pi. The lecture also touches on lossless information representation, introducing the Shannon–Fano algorithm for binary dichotomy based on appearance numbers. It highlights entropy as a bound on the average length of bits used to transmit information and hints at upcoming topics like Shannon's theorem, Huffman coding, and lossy codes.

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Related concepts (25)

Lossless compression

Lossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates (and therefore reduced media sizes).

Lossy compression

In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. The different versions of the photo of the cat on this page show how higher degrees of approximation create coarser images as more details are removed. This is opposed to lossless data compression (reversible data compression) which does not degrade the data.

Data compression

In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information.

Image compression

Image compression is a type of data compression applied to s, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data. Image compression may be lossy or lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics.

Entropy (information theory)

In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable , which takes values in the alphabet and is distributed according to : where denotes the sum over the variable's possible values. The choice of base for , the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannons"), while base e gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys".

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