Codes and turbo codes by Claude Berrou
By Claude Berrou
This publication is dedicated to at least one of the fundamental services of recent telecommunications structures: channel coding or mistakes correction coding. Its major subject is iteratively decoded algebraic codes, convolutional codes and concatenated codes. It additionally offers electronic modulation with which channel coding is heavily linked to make up the guts of the actual layer of telecommunications platforms. an important theoretical facets are given, and the construction of codes is exact and justified. interpreting algorithms are built and, at any time when attainable, followed by means of simulation effects attribute in their correcting power.The authors are researchers and teachers recognized for his or her services within the box of encoding and deciphering algorithms and linked circuits. Codes and faster Codes is meant either as a method for locating the area, a invaluable resource of data in regards to the many innovations imagined because the mid-XXth century, and as a step in the direction of addressing difficulties now not but solely solved.
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5 dB. ), when the MHD is not very high. Curve 3 shows performance with mediocre convergence and high asymptotic gain. A typical example of this is the concatenation of a Reed-Solomon code and of a convolutional code. Whereas the MHD can be very large (around 100, for example), the decoder can beneﬁt only relatively far from the theoretical limit. It is therefore not the quality of the code that is in question but the decoder, which cannot exploit all the information available at reception. 6 – Possible behaviours for a coding/decoding scheme on a Gaussian channel (k = 1504 bits, R = 1/2).
The modulated signal s(t) then has a narrow spectrum centred on f0 , which is what we want. The signal to be transmitted will in the sequel be called the modulating signal. Modulation makes one of the parameters a and ϕ vary as a function of 20 Codes and Turbo Codes the modulating signal if the latter is analogue. In the case of a digital signal, the modulating signal is a series of elements of a ﬁnite set, or symbols, applied to the modulator at discrete instants that are called signiﬁcant instants.
Performance is, of course, the main criterion: for a given error rate, counted either in BER or in PER and for a ﬁxed coding rate, a good code is ﬁrst the one whose decoder oﬀers a good error correction capability close to the corresponding theoretical limit. One preliminary condition of this is obviously the existence of a decoding algorithm (random codes do not have a decoder, for 1. Introduction 17 example) and that the software and/or hardware of this algorithm should not be too complex. Furthermore, using soft inputs could be an imperative that might not be simple to satisfy.