M.Sc Student | Dabbagh Amir |
---|---|
Subject | Sequential Signaling under Peak-Power Constraint in the Poisson Regime |
Department | Department of Electrical Engineering | Supervisor | Dr. Shraga Bross |
Sequential signaling over the single-user and two-user multiple-access Poisson channel subject to peak and average power constraints is considered. It is assumed that the information is transmitted in blocks, and the channel is corrupted by additive
constant dark current
with rate .
Furthermore, it is assumed that a noiseless delayless feedback link is employed
in the communication system. It is well known that feedback does not increase
the capacity of a single-user discrete memoryless channel as shown by Shannon (1967), and later generalized to continuous-time memoryless channels by Kadota
(1971). However, unbounded random transmission time codes can improve
significantly the attainable error exponent. In Schalkwijk and Barron (1971), a
sequential signaling scheme is proposed for the single-user peak-limited and
bandwidth unlimited additive white Gaussian noise channel. It improves on the
reliability function of the one-way infinite bandwidth AWGN channel Wyner
(1967), and the attainable error exponent for this signaling scheme is given by
where is the
permissible peak-to-average power ratio and
is the channel capacity.
For the ideal Poisson
channel Lapidoth (1993) showed that feedback improves on the fixed transmission-time
error exponent and attains zero error with random transmission-time codes. In
this work we analyze the performance of a sequential signaling scheme, similar to
the one proposed by Schalkwijk and Barron, for the Poisson channel. In the
single-user case and low power regime the error exponent is determined and it
is given by .
This exponent is attained with
. In the two-user multiple-access
case an attainable error exponent is established for the low power regime and
it is given by
where
is the rate sum capacity.
Again, this exponent is attained with
.