Cutoff rate for fixed-composition on-off keying over direct detection photon channels

Abstract

In this thesis, we consider direct detection photon channel with peak and average power constraints. This channel is modelled as a binary input discrete memoryless channel. We study the cutoff rate for different modulation formats on this channel since it is a measure of decoding complexity when sequential decoding is used and also, it gives an upper bound for the probability of error which decreases exponentially with the constraint length of convolutional code. Cutoff rates for the ensembles of fixed-composition and independent-letters codes along with ON-OFF keying are computed numerically and also some bounds are given. Cutoff rates versus signal-to-noise ratio or peak power are plotted for blocklengths of N=40,100 and for both ensembles. Comparison of cutoff rates for these two ensembles shows that for the direct detection photon channel the cutoff rate of fixed-composition ensemble is significantly greater than that of independent-letters ensemble for small values of signal-to-noise ratio and when the average power is a small fraction of peak power, say, 5-30%. In an uncoded system, for achieving a probability of error P(E)=(10 to the power -9), we should send 10 photons/slot with rate R=1 bit/slot, resulting in an efficiency of 0.1 bits/photon.However, using coding we can make probability of error arbitrarily small achieving an efficiency of 1 bit/photon. Also, some remarks on the implementation of fixed-composition trellis codes and on multi-level signalling instead of ON-OFF keying are given in conclusions.