Data Compression and Prefix-Free Codes

Data Compression and Prefix-Free Codes
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Error-Correcting Codes
Dig into different techniques for error correction. Start with a game called word golf, which demonstrates the perils of mistaking one letter for another and how to guard against it. Then graduate to approaches used for correcting errors in computer operating systems, CDs, and data transmissions from the Voyager spacecraft.
Unbreakable Codes and Public Keys
The one-time pad may be in principle unbreakable, but consider the common mistakes that make this code system vulnerable. Focus on the Venona project that deciphered Soviet intelligence messages encrypted with one-time pads. Close with the mathematics behind public key cryptography, which makes modern transactions secure--for now.
Neural Codes in the Brain
Study the workings of our innermost information system: the brain. Take both top-down and bottom-up approaches, focusing on the world of perception, experience, and external behavior on the one hand versus the intricacies of neuron activity on the other. Then estimate the total information capacity of the brain.
The Science of Information - From Language to Black Holes
The science of information is the most influential, yet perhaps least appreciated field in science today. Never before in history have we been able to acquire, record, communicate, and use information in so many different forms. Never before have we had access to such vast quantities of data of every…
The Transformability of Information
What is information? Explore the surprising answer of American mathematician Claude Shannon, who concluded that information is the ability to distinguish reliably among possible alternatives. Consider why this idea was so revolutionary, and see how it led to the concept of the bit--the basic unit of information.
Computation and Logic Gates
Accompany the young Claude Shannon to the Massachusetts Institute of Technology, where in 1937 he submitted a master's thesis proving that Boolean algebra could be used to simplify the unwieldy analog computing devices of the day. Drawing on Shannon's ideas, learn how to design a simple electronic circuit that performs…
Measuring Information
How is information measured and how is it encoded most efficiently? Get acquainted with a subtle but powerful quantity that is vital to the science of information: entropy. Measuring information in terms of entropy sheds light on everything from password security to efficient binary codes to how to design a…
Entropy and the Average Surprise
Intuition says we measure information by looking at the length of a message. But Shannon's information theory starts with something more fundamental: how surprising is the message? Through illuminating examples, discover that entropy provides a measure of the average surprise.
Encoding Images and Sounds
Learn how some data can be compressed beyond the minimum amount of information required by the entropy of the source. Typically used for images, music, and video, these techniques drastically reduce the size of a file without significant loss of quality. See how this works in the MP3, JPEG, and…
Noise and Channel Capacity
One of the key issues in information theory is noise: the message received may not convey everything about the message sent. Discover Shannon's second fundamental theorem, which proves that error correction is possible and can be built into a message with only a modest slowdown in transmission rate.
Signals and Bandwidth
Twelve billion miles from Earth, the Voyager spacecraft is sending back data with just a 20-watt transmitter. Make sense of this amazing feat by delving into the details of the Nyquist-Shannon sampling theorem, signal-to-noise ratio, and bandwidth--concepts that apply to many types of communication.
Cryptography and Key Entropy
The science of information is also the science of secrets. Investigate the history of cryptography starting with the simple cipher used by Julius Caesar. See how entropy is a useful measure of the security of an encryption key, and follow the deciphering strategies that cracked early codes.