We study lower bounds on mutual information that are achievable rates for optimal and sub-optimal hard-decision (HD) and soft-decision (SD) decoding. These rates represent the maximum amount of information we can convey over a memoryless channel with a fixed input if ideal forward error correction (FEC) is employed.
We find that the gain of complex SD decoding over HD decoding can be very small, depending on the modulation format and the system parameters. We further study the gap of a practical FEC scheme to its asymptotic limit.