Channel Coding: Theory, Algorithms, and Applications

(11)

where ${\mathbf{S}}_i$ is the encoder state after the encoding of bit $d_i$.

The LLR of bit $d_i$ can then be expressed as

$\mathrm{\Lambda }(d_i)=\ln \frac{{\mathrm{\Sigma }}_m{\lambda }_i^1(m)}{{\mathrm{\Sigma }}_m{\lambda }_i^0(m)}\text{.}$ (12)

(12)

For the code of Figure 26, $\mathrm{\Lambda }(d_i)$ is written as

$\mathrm{\Lambda }(d_i)=\frac{{\lambda }_i^1(0)+{\lambda }_i^1(1)+{\lambda }_i^1(2)+{\lambda }_i^1(3)}{{\lambda }_i^0(0)+{\lambda }_i^0(1)+{\lambda }_i^0(}$