Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement is unknown, and likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over classical- and nonclassical-state alphabets. We first review state-of-the-art coherent on-off-keying (OOK) and pulse-position modulation (PPM) with a photon-counting measurement, illustrating its asymptotic inefficiency relative to the Holevo limit. Then we analyze two architectures that improve upon the dimensional versus photon efficiency tradeoff achievable with conventional OOK or PPM. We show that at high photon efficiency these architectures achieve an efficiency tradeoff that differs from the best possible tradeoff by only a constant factor. The first architecture is a coherent-state transmitter that relies on feedback from the receiver to control the transmitted energy. The second architecture uses a single-photon number-state source.

We study the class of periodic-finite-type (PFT) shift spaces, which can be used to model time-varying constrained codes used in digital magnetic recording systems. A PFT shift is determined by a finite list of periodically forbidden words. We show that the class of PFT shifts properly contains all finite-type (FT) shifts, and the class of almost finite-type (AFT) shifts properly contains all PFT shifts. We establish several basic properties of PFT shift spaces of a given period$T$, and provide a characterization of such a shift in terms of properties of its Shannon cover (i.e., its unique minimal, deterministic, irreducible graph presentation). We present an algorithm that, given the Shannon cover${\cal G}$of an irreducible sofic shift$X$, decides whether or not$X$is PFT in time that is quadratic in the number of states of${\cal G}$. From any periodic irreducible presentation of a given period, we define a periodic forbidden list, unique up to conjugacy (a circular permutation) for that period, that satisfies certain minimality properties. We show that an irreducible sofic shift is PFT if and only if the list corresponding to its Shannon cover${\cal G}$and its period is finite. Finally, we discuss methods for computing the capacity of a PFT shift from a periodic forbidden list, either by construction of a corresponding graph or in a combinatorial manner directly from the list itself.

This paper presents and compares two iterative coded modulation techniques for deep-space optical communications using pulse-position modulation (PPM). The first code, denoted by SCPPM, consists of the serial concatenation of an outer convolutional code, an interleaver, a bit accumulator, and PPM. The second code, denoted by LDPC-PPM, consists of the serial concatenation of an LDPC code and PPM. We employ Extrinsic Information Transfer (EXIT) charts for their analysis and design. Under conditions typical of a communications link from Mars to Earth, SCPPM is 1 dB away from capacity, while LDPC-PPM is 1.4 dB away from capacity, at a Bit Error Rate (BER) of approximately 10-5. However, LDPC-PPM lends itself naturally to low latency parallel processing in contrast to SCPPM.

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. In systems utilizing photon-counting photodetectors, which are finding increased use, the detected process is well modeled as a Poisson point process. In this paper, we analyze the performance of maximum likelihood (ML) estimators of the arrival time of an optical pulse, based on observations of a Poisson process. We develop an analytic model for the mean-square error of the ML estimator, illustrating two phenomena that cause deviations from the Cramer-Rao bound at low signal photon flux. The model accurately predicts the ML performance over all regimes considered. We also derive an approximation to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time.

Significant technological advances were made toward utilizing the Hale telescope for receiving the faint laser communication signals transmitted from an optical transceiver on a spacecraft orbiting Mars. The so-called Palomar receive terminal design, which would have supported nominal downlink data rates of 1-30 Mbps, is described. Testing to validate technologies for near-Sun (3deg from edge of solar disc) daytime operations is also discussed. Finally, a laboratory end-to-end link utilizing a 64-ary pulse-position modulated photon-counting receiver and decoder that achieved predicted near-capacity (within 1.4 dB) performance is described.

We present an efficient implementation of a coded modulation for the deep space optical channel. NASA designed this so called serially concatenated pulse position modulation (SCPPM) code to provide an optical link that can operate within one dB signal energy of the Shannon capacity during a nominal mission condition from Mars. Here, we describe some of the challenges in realizing the SCPPM decoder on a field-programmable gate array (FPGA). Through various architectural optimizations, we achieve a 6 Mbps decoder on a single FPGA. Moreover, we demonstrate that it is possible to communicate reliably on an efficient bits-per-photon count in an end-to-end SCPPM coded system.

We describe novel interleaver and deinterleaver architectures that support bandwidth efficient memory access for decoders of turbo-like codes that are used in conjunction with high order modulations. The presentation focuses on a decoder for serially concatenated pulse-position modulation (SCPPM), which is a forward-error-correction code designed by NASA to support laser communications from Mars at mega-bits-per-second (Mbps) rates. For 64-ary PPM, the new architectures effectively triple the fan-in of the interleaver and fan-out of the deinterleaver, enabling parallelization that doubles the overall throughput. The techniques described here can be readily modified for other PPM orders

We show the capacity of a generalized pulse position modulation (PPM) channel, where the input vectors may be any set that allows a transitive group of coordinate permutations, is achieved by a uniform input distribution. We derive a simple expression for capacity in terms of the Kullback-Leibler distance for the binary case, and find the asymptote in the PPM order. We prove a subadditivity result for the PPM channel and use it to show PPM capacity is monotonic in the order.

We examine several properties of n-pulse pulse position modulation (PPM) [H. Sugiyama et al., 1989] on memoryless channels. We derive the maximum likelihood decision rule and an exact expression for the symbol error rate for nges1, generalizing previous results [R.M. Gagliardi et al., 1976, M. Simon et al., 2003]. A capacity comparison indicates that muItipulse PPM does not produce appreciable gains over conventional PPM except at high average power

Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the growth rate, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive a new algorithm for determining the joint spectral radius of sets of nonnegative matrices and combine it with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice.

Two algorithms for characterization of input error events producing specified distance at the output of certain binary-input partial-response (PR) channels are presented. Lists of error events are tabulated for PR channels of interest in digital recording.