1. { k1}  km exp { xk . uk1 + yk . Vk1,m } k+1f(1,m) m { k0} km exp { xk . uk0 + yk . Vk0,m }k+1f(0,m) m  km exp { yk . Vk1,m } k+1f(1,m) m { k} exp { 2xk }  km exp { yk . Vk0,m }k+1f(0,m) m  LLR  L( dk ) = L(dk) + { 2xk } + Log [ke ] Iterative decoding steps  Likelihood Ratio  ( dk ) = = = { k} exp { 2xk } { k e}

2. ki,m = ke i exp { xk . uki + yk . Vki,m }  km k1,m k+1f(1,m)  km k0,m k+1f(0,m) m m Iterative decoding • For the second iteration; • Calculate LLR for all times  Log Likelihood Ratio  L( dk ) = Log • Hard decision based on LLR after multiple iterations

3. Rayleigh fading channel

4. Rayleigh fading channel

5. Rayleigh fading channel model

6. Channel measurement based LLR • When no CSI is available in the decoder, the equation can be approximated by a Gaussian distribution with a mean x·Ea [a]=0.8862 x , and a variance σ2. The variance σ2 is determined by the additive noise. • If the decoder has knowledge of the fading amplitudes for each symbol, we can apply the Gaussian distribution with a mean axand a variance σ2.

7. Channel measurement based LLR

8. Performance Comparison

9. Performance Comparison

10. Performance Comparison

11. Performance Comparison • Effect of block size • Effect of channel fading • Effect of channel correlation • Importance of interleaver