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As pointed out in 2, the triple repetition code has a low code rate Rc = 1/3 that produces a poor BER performance, which is even worse than uncoded transmission, if a harddecision decoder is utilized A curious phenomenon is seen in Figure 625, where the BER performance of the triple repetition code using a soft-decision decoder is practically coincident with that of uncoded transmission This is so because, at the end of the day, the triple repetition of a given bit is the same as to transmit it with a signal of three times more energy than in the case of uncoded transmission The soft-decision decoder takes advantage of this additional energy, so that repetition is in a way equivalent to an increase in the number of output levels of the detector to more than 2.



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The Caesar cipher takes each letter and replaces it by the letter three places ahead where the alphabet is seen as cyclic (see section 1.1 of Abraham Sinkov's Elementary Cryptanalysis [ 1101 for a discussion). Hence, D replaces A , E replaces B , ..., B replaces Y, and C replaces Z . Use t r / / / to accomplish this. DNA are long molecules that contain sequences of four bases, which are abbreviated as A, T, C, and G. DNA is double stranded, and the bases in one strand have the following relationship with the bases in the other: A and T always pair up as well as C and G. For example, given the fragment ATTTCTG, then the other strand must be TAAAGAC. Try implementing this conversion in Perl using tr/ACGT/TGCA/. Note that the letter translations are all done in parallel. Although the above DNA sequence is made up, there are vast amounts of real DNA sequences available at the National Center for Biotechnology Information (NCBI) via their Web page: h t t p ://www .ncbi .nlm. n i h . gov/ [8 11. For information on using Perl to analyze DNA, see the excellent book Perl for Exploring DNA by Mark LeBlanc and Betsey Dexter Dyer [70].

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Here are a few of the terms that you should know to effectively support hard disk drive interfaces:

As pointed out above, the improvement of applying soft decision is not very signi cant for more than eight levels at the output of the soft-decision channel From this explanation it can be concluded that the triple repetition code is equivalent to uncoded transmission if the redundancy added is understood as an increase of the bit energy, a fact that should be taken into account in order to make a fair comparison of BER performances This increase in the energy per bit, which is determined by the rate Rc of the code, is a penalty that must be offset against the gain in performance offered by the error-correcting power of the code Seen in a rather different way, the triple repetition code is equivalent to uncoded transmission where each bit is sampled three times at the detector.

9. For adaptive filters with error nonlinearities,

Figure 12.11: Schematic of a single cancellation stage for user IC in the parallel interference cancellation (PIC) receiver for K users. The data estimates, d ( ' ) , . . . , d ( K - l ) of the other ( K - 1) users were obtained from the previous cancellation stage and the received sig-

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In the case of soft-decision decoding, the decoder uses the values of these three samples to evaluate the Euclidean distance over an AWGN channel When its use is possible, soft-decision decoding provides a better BER performance than that of hard-decision decoding of the same code, for all the coding techniques presented in previous chapters Sometimes, however, it is impractical to use soft-decision decoding, as discussed previously In the case of very long block length RS codes, for example, even softdecision trellis decoding has an implementation complexity which makes it impractical for most applications..

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