By Alain Glavieux
This publication offers a accomplished review of the topic of channel coding. It begins with an outline of data concept, concentrating on the quantitative size of data and introducing primary theorems on resource and channel coding. the fundamentals of channel coding in chapters, block codes and convolutional codes, are then mentioned, and for those the authors introduce weighted enter and output interpreting algorithms and recursive systematic convolutional codes, that are utilized in the remainder of the ebook.
Trellis coded modulations, that have their basic functions in excessive spectral potency transmissions, are then lined, prior to the dialogue strikes directly to a complicated coding method referred to as turbocoding. those codes, invented within the Nineties through C. Berrou and A. Glavieux, exhibit remarkable functionality. the diversities among convolutional turbocodes and block turbocodes are defined, and for every kinfolk, the authors current the coding and interpreting strategies, including their performances. The ebook concludes with a bankruptcy at the implementation of turbocodes in circuits.
As such, somebody all for the parts of channel coding and mistake correcting coding will locate this ebook to be of helpful assistance.Content:
Chapter 1 details thought (pages 1–40): Gerard Battail
Chapter 2 Block Codes (pages 41–128): Alain Poli
Chapter three Convolutional Codes (pages 129–196): Alian Glavieux and Sandrine Vaton
Chapter four Coded Modulations (pages 197–253): Ezio Biglieri
Chapter five Turbocodes (pages 255–306): Claude Berrou, Catherine Douillard, Michel Jezequel and Annie Picart
Chapter 6 Block Turbocodes (pages 307–371): Ramesh Pyndiah and Patrick Adde
Chapter 7 Block Turbocodes in a pragmatic environment (pages 373–414): Patrick Adde and Ramesh Pyndiah
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Additional info for Channel Coding in Communication Networks: From Theory to Turbocodes
This probability is greater than that of a decoding error, but in a coarsely exaggerated fashion because, if f ≥ dmin /2, such an error occurs only if in a space with n dimensions provided by the Hamming metric, the conſguration of occurring errors goes exactly in the direction of another codeword, which is at the minimum distance dmin from the transmitted 26 Channel Coding in Communication Networks codeword. However, the redundancy of code means that its codewords are rare in En , and much more so are the codewords at a minimum distance from a given codeword, which makes this occurrence highly improbable.
The demonstration of this inequality is very easy for an irreducible code. Let nN be the largest length of codewords. It is sufſcient to note that the set of all the codewords of length nN written with an alphabet of q symbols can be represented by all the paths of a tree where q branches diverge from a single root, q branches then diverge from each end, and so on until the length of the paths in the tree reaches nN branches. There are q nN paths of different lengths Information Theory 17 nN . When the ith codeword is selected as belonging to the code, the condition that no codeword is the preſx of any other codeword interdicts the q nN −ni paths whose ſrst ni branches represent the ith codeword.
11], which expresses that we use all 18 Channel Coding in Communication Networks possible codewords compatible with decodability, which we will suppose; and also pi = qi for all i, that is ni = − log(pi )/ log(q), 1 ≤ i ≤ N ; if there are N integers verifying this condition, the coding is referred to as absolutely optimal. 12] it is enough to multiply by pi and to sum up for i from 1 to N . 1 (THE FUNDAMENTAL THEOREM OF SOURCE CODING ). For any stationary source there is a decodable coding process where the average length n of codewords per source symbol is as close to its limit lower H/ log(q) as we wish.
Channel Coding in Communication Networks: From Theory to Turbocodes by Alain Glavieux