Research Article
Log-Likelihood Ratio Calculation for Iterative Decoding on Rayleigh Fading Channels Using Padé Approximation
Table 1
The coefficients of LLR approximation functions for 8-PAM at SNR = 7.91 (
).
(a) Taylor series of order |
| | | | | | |
| bit 1 | 0.0 | 0.0 | 1.2135 | 0.0 | 0.0241 | bit 2 | 3.3449 | 2.3273 | −0.7706 | 0.0205 | 0.0006 | bit 3 (a) | 1.8848 | −0.7855 | 0.0544 | 0.2848 | −0.0491 | bit 3 (b) | 6.9832 | 2.2528 | −0.2497 | −0.0181 | 0.0011 |
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(b) Padé approximation of numerator |
| | | | | | | | | | |
| bit 1 | 0.0 | 0.0 | 1.2135 | 0.0 | 0.0334 | 0.0 | 0.0025 | 0.0 | | bit 2 | 3.3449 | 3.3382 | −1.5496 | 0.1836 | 0.0039 | −0.0028 | — | — | — | bit 3 (a) | 1.8848 | −1.1396 | 0.6046 | — | — | — | — | — | — | bit 3 (b) | 6.9832 | 5.6135 | −3.1331 | 0.5963 | −0.0481 | 0.0017 | — | — | — |
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(c) Padé approximation of denominator |
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| bit 1 | 0.0000 | 1.0000 | 0.0000 | 0.0076 | 0.0000 | 0.0016 | bit 2 | 3.3449 | 1.6585 | −0.3831 | 0.0557 | — | — | bit 3 (a) | 1.8848 | 1.4533 | −0.6204 | 0.3220 | −0.0852 | 0.0113 | bit 3 (b) | 6.9832 | 1.3191 | −0.5502 | 0.0496 | −0.0026 | — |
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