I'd need to know how to estimate the log-likelihood ratio of a m-ary symbol to apply message passing decoding on it on AWGN channel.
For the BPSK case, we know that it is $L(u_n)=2y_n/σ^2$. But how shall we proceed when we have other modulation orders, such as QPSK, 8-PSK, 16-APSK and 32-APSK (The ones appearing in DVB-S2 standard)?
I came across one formula appearing as an answer to this question but as stated there only serves for QAM. Also it has been negatively voted and has no reference whatsoever so cannot be sure about it.
Could anyone lend me a hand with this?
Many thanks in advance, and BR.