Is there an optimal way to quantize log-likelihood ratios of an AWGN channel?
It depends on your actual decoder architecture, but if memory serves me right, uniform quantization is optimal for Min-Sum or Sum-Product decoders. (Intuitively, kind of makes sense – any other quantization could be modelled as &quot;let's first apply a function to the LLRs and then quantize the result of that uniformly&quot;, and LLRs are what asymptotically achieves maximum likelihood performance.)
The question is where you put your quantization boundaries: If you have a fixed number of bits for your LLRs, do you quantize the region from, say, $-2\sigma$ to $+2\sigma$, because everything larger is sufficiently &quot;safely&quot; the sign-indicated value, anyway? Or do you have a large code word length, and you want to make sure that in sea of large LLRs, where some represent bit errors, the &quot;righter&quot; ones are
still understood as such?
That's a question of looking your design SNR and your target FER; no general answer or formula is known, far as I'm aware.