The cutoff rate for on-off keying

It is well known that on-off keying (OOK), i.e. the transmission of a pulse for a data one (mark) and transmission of no signal for a data zero (space), exhibits a 3 dB inferiority to antipodal signalling, in terms of the signal-to-noise ratio required to achieve a specified bit error probability. When the channel is characterized by the cutoff rate R₀, this 3 dB inferiority persists, in the sense that the required E_b/N₀ to operate at a given value of R₀ is 3 dB greater for the OOK channel than for the antipodal channel. However, it is shown that, if the definition of cutoff rate is generalized in an appropriate way to reflect the fact that signal energy is expended only in the transmission of marks, part of this penalty is recovered. In fact, it is shown that, in the limit of low R₀, there is no penalty in signal-to-noise ratio. Even at rates of realistic interest, the penalty is significantly less than the expected 3 dB