By George C. Clark Jr., J. Bibb Cain
Error-correction coding is getting used on a nearly regimen foundation in such a lot new conversation structures. not just is coding apparatus getting used to extend the strength potency of conversation hyperlinks, yet coding principles also are offering cutting edge ideas to many similar conversation difficulties. between those are the removal of intersymbol interference brought on by filtering and multipath and the enhanced demodulation of convinced frequency modulated indications through profiting from the "natural" coding supplied via a continuing section. even supposing numerous books and nu merous articles were written on coding idea, there are nonetheless obvious deficiencies. First, the sensible elements of translating a particular deciphering set of rules into genuine were principally missed. the data that's on hand is sketchy and is generally dispersed. moment, the data required to guage a selected process lower than events which are en countered in perform is obtainable for the main half purely in inner most corporation studies. This ebook is geared toward correcting either one of those difficulties. it really is written for the layout engineer who needs to construct the coding and deciphering apparatus and for the conversation process engineer who needs to contain this apparatus right into a method. it's also appropriate as a senior-level or first-year graduate textual content for an introductory one-semester path in coding thought. The ebook U"Ses no less than arithmetic and fully avoids the classical theorem/proof strategy that's usually obvious in coding texts.
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Additional info for Error-Correction Coding for Digital Communications
Different values of B simply correspond to taking different bases for the logarithm and thus provide a convenient means of adjusting the scale of the metric. In the case of the hard decision channel A and B can be adjusted so that the metric values are 0 and 1. Thus, the metric corresponds exactly to the number of errors, and choosing the code word which contains the smallest number of errors is indeed an optimum strategy. One may observe that the ability to define a metric is independent of the underlying noise process.
This last strategy is equivalent to not performing error detection. Equations (1-15) through (1-18) are probably impossible to evaluate except for very small values of k. Fortunately, when the block code is also a group code, they can be simplified significantly. In order to carry out this simplification process, we will have to use properties of group codes that have not yet been developed. Hopefully, the reader will be willing to proceed on faith until the necessary justification is supplied in Chapter 2.
Therefore, one must conclude that the (63,51) code is a good code and little improvement could be obtained by further searching. Table 1-4 provides upper and lower bounds on k for different values of n and d. The values of kmax were obtained using the Hamming bound except those values marked with an asterisk where the Plotkin bound provides a tighter value. Lower bounds are obtained using the Gilbert bound Also included in this table are parameters associated with some known constructable BCH codes.