# Foundations of Coding: Compression, Encryption, Error Correction

## Jean-Guillaume Dumas, Jean-Louis Roch, Éric Tannier, Sébastien Varrette

Language: English

Pages: 450

ISBN: B00STERUWA

Format: PDF / Kindle (mobi) / ePub

**Offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations**

This book offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations. This text focuses on the ways to structure information so that its transmission will be in the safest, quickest, and most efficient and error-free manner possible. All coding operations are covered in a single framework, with initial chapters addressing early

mathematical models and algorithmic developments which led to the structure of code. After discussing the general foundations of code, chapters proceed to cover individual topics such as notions of compression, cryptography, detection, and correction codes. Both classical coding theories and the most cutting-edge models are addressed, along with helpful exercises of varying complexities to enhance comprehension.

Foundations of Coding: Compression, Encryption,Error-Correction is an invaluable resource for understanding the various ways information is structured for its secure and reliable transmission in the 21st-century world.

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codes and have a distance 5. Solution on page 338. Exercise 4.41 (Decoding of a CIRC on an Audio CD) We now consider the codes and over of the CIRC on audio CDs. The purpose of this exercise is to give the details of the steps of decoding. When one receives a block of 32 bytes, explain how to erase a block or to correct at most one error with the code using the calculus of the error syndrome. During the decoding with , explain how to correct at most four erasures. Solution on page 338.

some distortion due to the transmission. Figure 1 Encoding of a message M The recipient applies If an error cannot be corrected, its detection might lead to an automatic return of the message to the issuer. Figure 2 Decoding of a message The message does not contain any information item which would enable one to recover M without having the correct functions. However, it must contain some information items to check its coherency and possibly to correct it. Finally, it must be as small as

lost. In order to sign an e-mail, one must use one's private key, which has been lost. Therefore, it is impossible. On the contrary, it is still possible to check a signature as it only requires recovering the public key in the certificate of the sender. Exercise 3.36 (on page 201) Since you have complete trust in Alice, you can be sure of Bob's certificate. However, you know nothing of Bob's certification policy. Therefore, you cannot be sure that the message was actually issued by Oscar.

protocol? Solution on page 309. The most classic attack on interchange protocols consists in Oscar cutting the communication line between Alice and Bob before they start the key sharing (transmission of A and B). This is the so-called Man-in-the- middle attack. The general idea is that Oscar passes himself off as Bob as far as Alice is concerned and as Alice as far as Bob is concerned. In this way, Oscar can read all communications between Alice and Bob with the key that they think they have

and Shortened Codes As the distance characterizes the number of errors that can be corrected by a code, it is an important characteristic, complementary to its rate. In order to choose trade-offs between the rate and the distance, several methods enable one to modify a code in order to build another code with different properties. 4.3.2.1 Equivalent Codes Let and be two codewords: let be a permutation of the indexes ; one has let be n permutations of the symbols in V (which are possibly