Jon Hamkins

Asymptotically dense spherical codes. I. Wrapped spherical codes

A new class of spherical codes called wrapped spherical codes is constructed by wrapping any sphere packing /spl Lambda/ in Euclidean space onto a finite subset of the unit sphere in one higher dimension. The mapping preserves much of the structure of /spl Lambda/, and unlike previously proposed maps, the density of the wrapped spherical codes approaches the density of /spl Lambda/ as the minimum distance approaches zero. We show that this implies that the asymptotically maximum spherical coding density is achieved by wrapped spherical codes whenever /spl Lambda/ is the densest possible sphere packing.

Asymptotically dense spherical codes .II. laminated spherical codes

For pt. I see ibid., vol.43, no.6, p.1774-85, 1997. New spherical codes called laminated spherical codes are constructed in dimensions 2-49 using a technique similar to the construction of laminated lattices. Each spherical code is recursively constructed from existing spherical codes in one lower dimension. Laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes. The density of a laminated spherical code approaches the density of the laminated lattice in one lower dimension, as the minimum distance approaches zero. In particular, the three-dimensional laminated spherical code is asymptotically optimal, in the sense that its density approaches the Fejes Toth (1959) upper bound as the minimum distance approaches zero. Laminated spherical codes perform asymptotically as well as wrapped spherical codes in those dimensions where laminated lattices are optimal sphere packings.

Selection of modulation and codes for deep-space optical communications

We describe several properties of deep space optical channels that lead to an appropriate selection of modulation format, pulse position modulation (PPM) order, error control code rate, and coding scheme. The selection process is motivated by capacity considerations. We compare the Shannon limit to the performance of Reed-Solomon codes and convolutional codes concatenated with PPM and show that, when iteratively decoded, concatenated convolutional codes operate approximately 0.5 dB from capacity over a wide range of signal levels, about 2.5 dB better than Reed-Solomon codes.

A decoder architecture for high-speed free-space laser communications

We present a decoding architecture for high-speed free-space laser communications. This system will be used by NASAs Mars Laser Communication Demonstration (MLCD) project, the first use of high-speed laser communication from deep space. The Error Correction Code (ECC) and modulation techniques for this project have been motivated by an analysis of capacity, and existing designs have been shown to operate within 0.9 dB of the Shannon limit on the nominal operating point. In this paper, we give the algorithmic description and FPGA implementation details that led to the development of a 50 Mbps hardware decoder.

EXIT Function Aided Design of Iteratively Decodable Codes for the Poisson PPM Channel

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.

Constrained coding for the deep-space optical channel

We investigate methods of coding for a channel subject to a large dead-time constraint, i.e., a constraint on the minimum spacing between transmitted pulses, with the deep-space optical channel as the motivating example. Several constrained codes designed to satisfy the dead-time constraint are considered and compared on the basis of throughput, complexity, and decoded error-rate. The performance of an iteratively decoded serial concatenation of a modulation code with an outer code is evaluated and shown to provide significant gains over Reed-Solomon concatenated with Pulse Position Modulation.

Laboratory characterization of silicon avalanche photodiodes (APD) for pulse position modulation (PPM) detection

Two commercially available large area silicon avalanche photodiodes (APD) were characterized in the laboratory. The response of the APDs to a sequence of 8-bit pulse position modulated (256-PPM) laser pulses, with and without additive background noise, was recorded and stored for post analysis. Empirical probability density functions (pdfs) were constructed from the signal and noise slot data and compared to pdfs predicted by an analytical model based on Webb+Gaussian statistics. The pulse sequence was used to generate bit-error rate (BER) versus signal photons per pulse plots, albeit with large error bars due to the limited number of signal pulses stored. These BER measurements were also compared with analytical results obtained by using the Gaussian and Webb+Gaussian models for APD channel statistics. While the measurements qualitatively reflect features predicted by theory, significant quantitative deviations were displayed between the measurements and theory. The source of these discrepancies is not currently well understood, but it is surmised that inaccurate knowledge of detector parameters such as gain and noise equivalent temperature models may explain the discrepancies.

Capacity of avalanche-photodiode-detected pulse position modulation

The capacity is determined for an optical channel employing Pulse Position Modulation (PPM) and an Avalanche PhotoDiode (APD) detector. This channel is different from the usual optical channel in that the detector output is characterized by a Webb-plus-Gaussian distribution, not a Poison distribution. The capacity is expressed as a function of the PPM order, slot width, laser dead time, average number of incident signal and background photons received, and APD parameters. Based on a system using a laser and detector proposed for X2000 second delivery, numerical results provide upper bounds on the data rate and level of background noise that the channel can support while operating at a given BER. For the particular case studied, the capacity-maximizing PPM order is near 2048 for nighttime reception and 16 for daytime reception. Reed-Solomon codes can handle background levels 2.3 to 7.6 dB below the ultimate level that can be handled by codes operating at the Shannon limit.

Formulation of Modulation Recommendations for Future NASA Space Communications

The National Aeronautics and Space Administration (NASA) has recently conducted a comprehensive study to identify the most appropriate and efficient modulation, coding, multiple access and link protocol techniques for future space communication links supporting space exploration and science missions. The study was chartered by NASAs space communication and navigation (SCaN) office and is referred to as the coding, modulation, and link protocol (CMLP) study. This paper describes the CMLP modulation evaluation and states the relevant conclusions and recommendations.

Fading Losses on the LCRD Free-Space Optical Link Due to Channel Turbulence

The Laser Communications Relay Demonstration (LCRD) will implement an optical communications link between a pair of Earth terminals via an Earth-orbiting satellite relay. Optical turbulence over the communication paths will cause random uctuations, or fading, in the received signal irradiance. In this paper we characterize losses due to fading caused by optical turbulence. We illustrate the performance of a representative relay link, utilizing a channel interleaver and error-correction-code to mitigate fading, and provide a method to quickly determine the link performance.