Aspects of the present disclosure are directed in part to a receiver DSP unit including an equalization module. The equalization module includes a trellis-based equalization module that may utilize multiple trellis-based processors (TBP), which can each be individually adaptively configured for performing a trellis-based equalization. The design of the TBPs allows them to be configured for compensating a residual Inter-Symbol Interference (ISI) as well as compensating a residual Phase Noise (PN). ISI is an example of an additive impairment and PN is an example of a multiplicative impairment that communication systems, particularly high speed transmission systems such as coherent optical systems, can suffer from.