Several aspects of problems encountered in coding applications
The applications of encoding cover some very large domains, such as telecommunications, by hertzian or guided channels, magnetic recording, instrumentation, teledetection, confidentiality...where a set of chronic problems appear.
An analysis of the principles issues follows.
The theorician defines codes which have properties stemming from their algebraic structure, and their exploitation allows the correction of a finite number of error configurations in decoding. Firstly, the implementation of procedures come up against material constraints of the complexity and rapidity of the calculations. In this domain, the rapid evolution of technology since 1970 has allowed for the implementation of powerful codes and in the near future we can already foresee the large growth of possibilities. However, the principle problems appear essentially in the actual choice of the codes used. The error configurations depend, in the transmission channels, on the energy distribution of a bit of information and on the distribution of noise in the channel in the time-frequency domain, and the characteristics of the signal used. The use of linear codes is often adopted, but if the cyclic codes, for which the mathematic tool is better adjusted, are frequently chosen, the convolutive codes reserve inviting aspects for the user thanks to their possibilities in exploiting weighted decisions. Finally, in certain cases, only the non-linear codes are susceptible to resolve the problems posed by the characteristics of actuel channels.
The choice in coding, in practice, results in a compromise which takes into account the mastering of developped techniques on known codes, the complexity of the material, the rapidity of processing and an estimation of error patterns. A different approach, but which is generally not used, consists in determining code characteristics using those from the transmission channel. This approach, which implies a more precise definition of the channel and specific research of codes leads to a more rational conception of systems. These additional techniques, like interleaving, combine to make the correction of certain error patterns casier.
Some examples show the effectiveness of encoding but also bring out its weaknesses.
They repose the crucial question of the cost of implantation of a code in a system faced with the solutions of substitution.
KeywordsError Probability Power Density Spectrum Transmission Channel Cyclic Code Convolutional Code
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