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Expressions for the cutoff rate of memoryless channels and certain channels with memory are derived assuming decoding with approximate channel statistics. For channels with memory, two different decoding techniques are examined: conventional decoders in conjunction with ideal interleaving/deinterleaving, and maximum likelihood decoders that take advantage of the channel memory. As a practical case of interest, the cutoff rate for the band-limited nonlinear satellite channel is evaluated where the modulation is assumed to be M-ary phase shift keying (MPSK). The channel nonlinearity is introduced by a limiter in cascade with a traveling wave tube amplifier (TWTA) at the satellite repeater while the channel memory is created by channel filters in the transmission path.