Table 1 Summary of the chip-level turbo combining algorithm

Initialize ${\underset{¯}{\tilde{\mathbf{y}}}}_f^{\left(0\right)}$ and ${\underset{¯}{\mathbf{D}}}_i^{\left(0\right)}$ with ${\mathbf{0}}_{T_c{N}_T\times 1}$ and ${\mathbf{0}}_{N_T\times N_T}$, respectively.

1.

Combining at round k

1.1. Update ${\underset{¯}{\tilde{\mathbf{y}}}}_f^{\left(k\right)}$and ${\underset{¯}{\mathbf{D}}}_i^{\left(k\right)}$according to (25) and (26).

1.2. At each iteration,

   1.2.1 Compute the forward and backward filters using (28) and (29).

   1.2.2 Compute the MMSE estimate of x _f using (27).

   1.2.3 Compute extrinsic LLRs ${\varphi }_{t,j,m}^{\left(e\right)}$according to (17).

1.3. end 1.2.