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In order to identify the potentially most reliable channel quality measure to be used in our BbB adaptive turbo-coded QAM modems to be designed during our forthcoming discourse, we will now analyse the relationship between the average burst LLR magnitude before and after channel decoding For this reason, the random turbo interleaver size reduced from was the previously used 9984 bits and it was varied on a BbB basis, corresponding to the modulation mode used, as shown in Table 105, in order to enable BbB decoding so that we could obtain the average burst LLR magnitude of the coded data burst corresponding to the uncoded data burst Explicitly, the interleaver size is set to be equivalent to the number of source bits in a data burst, in order to enable BbB decoding Since the code rate is 0.



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the gods worshipped at its altars If a State suffered reverses, then the prestige of its gods declined in the same measure and vice versa Public religion and civic morals were fused: they were but different aspects of the same reality To bring glory to the City was the same as enhancing the glory of the gods of the City: it worked both ways Now, the phenomena in the religious sphere can be recognized because they are wholly unlike those of the human order They belong to a world apart The individual qua individual is part of the profane world, whilst the gods are the very nucleus of the religious world, and between these two worlds there is a gulf The gods are, in their substance, different from men: they have other ideas, other needs and an existence with no likeness to that of men.





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72 and the number of coded bits is 684, 1368, 2736 and 4104 for BPSK, 4-QAM, 16-QAM and 64-QAM, respectively, for a burst length of 684 symbols, the interleaver size(= number of source bits = number of coded bits - number of parity bits) is as shownin Table 105 The average burst LLR magnitude is defined as follows: (1016) where L b is the number of data bits per transmitted burst and U , is the ith data bit in the burst Figure 1012 shows the improvement of the average burst LLR magnitude after turbo decoding for the turbo BCH codec Table 103 over the wideband Rayleigh fading channel of environment of Table 104.

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As seen in the figure, the gradient of the curve is approximately unity for the average burst LLR magnitude before decoding over the range 5 for BPSK of 0 to and 4-QAM, 0 to 6 for 16-QAM and 0 to 10 for 64-QAM Thus, there is no average LLR magnitude improvement upon introducing turbo decoding in this low reliability range This is in harmony with our previous observations Figures 1010and 10 I 1, namely that thereis in no BER improvement for BERs below10-l Beyond this range, there is a sharp increase in the decoded LLR magnitude due to turbo decoding Figure 1012(a) also shows the effect of increasing the numberof decoder iterations on the average burst LLR magnitude Increasing the numberof decoder iterations improves not only the BER, also the average confidence but measure of the decoder s decisions Figure 10.

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13 shows the relationship between the estimated short-term BER defined in Equation 1015 and the average burst LLR magnitude after turbo decoding using six iterations Note that the curves becomes more spread out , as the short-term BER decreases This is because the relationship between the probability bit error in the decoded burst of expressed in the logarithmic domain inversely proportional to LLR magnitude,as shown is its in Figure 1014 The average of the burst LLR magnitude is dominated by the LLR values of the bits having lower probability of bit error, whereas the short-term BER of the burst is dominated by the bits with higher probability of bit error The variance of the LLR values of the bits in the burst accounts for the spread of the the estimated short-term BER versus average burst LLR magnitude curves Figure 1013 at low short-term BER values.

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