Channel Coding in Communication Networks docx

[...]... 1.2.2 Channel coding The goal of channel coding is completely different: to protect the message against channel noise We insist on the need for taking channel noise into account to the point of making their existence its specific property If the result of this noise is a symbol error probability incompatible with the specified restitution quality, we propose to transform the initial message by such a coding. .. this coding is very susceptible to noise, since each of its symbols is essential to the integrity of information It is therefore necessary to carry out channel coding making the message emerging from the source encoder (ideally) invulnerable to channel noise, which necessarily implies reintroducing redundancy We can suppose that source coding has been carried out in an ideal fashion; the only role of channel. .. “error correcting codes”, to which a large part of this book will be dedicated However, it is generally true that protection against noise is achieved only by introducing redundancy, as demonstrated in section 1.5.3 The objectives of source coding and channel coding thus appear to be incompatible They are even contradictory, since source coding increases the vulnerability to errors while improving concision... priori We will now examine what these properties are, and what these transformations, known as coding procedures, consist of and how, in particular, to carry out the standardization of the “source”, channel and “recipient” blocks introduced above We may a priori envisage transforming a digital message by source coding, channel coding and cryptography 1.2.1 Source coding Source coding aims to achieve...x Channel Coding in Communication Networks 3.7 Performance of convolutional codes 3.7.1 Channel with binary input and continuous output 3.7.1.1 Gaussian channel 3.7.1.2 Rayleigh channel 3.7.2 Channel with binary input and output 3.8 Distance spectrum of convolutional codes ... and the set 4 Channel Coding in Communication Networks of the receiving equipment and the recipient, on the other hand, may be interpreted as a new source-recipient pair adapted to the initial channel (Figure 1.2b) We can also consider the set of the transmitting equipment, the channel and the receiving equipment to constitute a new channel, adapted to the source-recipient pair provided initially (Figure... the means of ensuring decodability let us mention, without aiming to be exhaustive: – coding in blocks where all codewords resulting from coding have the same length, – addition of an additional symbol to the alphabet with the exclusive function of separating the codewords, – the constraint that no codeword is the prefix of another, that is to say, identical to its beginning Coding using this last means... applications xvi Channel Coding in Communication Networks Shannon had shown in 1948 that there exists a bound for the possible information flow in the presence of noise, the capacity of the channel, but had not clarified the means of dealing with it If the asymptotic nature of the Shannon theorem did not leave any hope to effectively reach the capacity, the attempts to approach it had remained in vain despite... content, i.e information, and deals with two operations essential for communication techniques: source coding and channel encoding Its main results are two fundamental theorems related to each of these operations The possibility of channel encoding itself has been essentially revealed by information theory That shows, to which point a brief summary of this theory is essential for its introduction Apart... simple and convincing illustration of the turbo effect 5.3 Turbocodes 5.3.1 Coding 5.3.2 The termination of constituent codes 5.3.2.1 Recursive convolutional circular codes 5.3.3 Decoding 5.3.4 SISO decoding and extrinsic information 5.3.4.1 Notations 5.3.4.2 Decoding using the MAP . Channel Coding in Communication Networks This page intentionally left blank Channel Coding in Communication Networks From Theory to Turbocodes Edited by Alain. binary symmetric channel 21 1.5.4.1. Hamming’s metric 21 1.5.4.2. Decoding with minimal Hamming distance 22 vi Channel Coding in Communication Networks 1.5.4.3. Random coding 23 1.5.4.4 prepared? 108 2.6.6. Hard decoding, soft decoding and chase decoding 110 2.6.6.1. Hard decoding and soft decoding 110 2.6.6.2. Chase decoding 110 2.7. 2D codes 111 2.7.1. Introduction 111 2.7.2.