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We present new codes and modulation formats for the deep space optical channel. By taking maximum avdvantage of inherent physical constraints on the communications link, these codes and modulation formats substantially close the large gap between state of the art systems and the Shannon limit.
The NASA Orion O2O mission was designed and tested to support high-rate bi-directional optical communications between one of multiple ground sites and a crewed capsule during a 10-day mission. This paper focuses on the design and performance of the receiver that will be based at the NASA White Sands Complex, New Mexico, USA. The main receiver components consist of two 40-cm apertures, each coupled to a specialty multi-mode optical fiber; each fiber coupled to a custom array of superconducting nanowire single-photon detectors; a high-speed, high-channel-count time-to-digital converter; and custom digitizing electronics to perform deserialization, demodulation, clock recovery, and forward error correction with a powerful serially-concatenated pulse-position-modulation turbo code. We show error-free data communication performance up to the maximum required data rate of 267 Mb/s.
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.
A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.
We present a field programmable gate array code (FPGA) implementation of a turbo-like decoder for a serially concatenated pulse-position modulation (SCPPM) code. NASA a developed this coded modulation scheme for deep space communications from Mars. Under a nominal mission condition, the decoder complexity by iteratively decoding the modulation and SCPPM coded system can operate within a one dB signal energy gap from capacity. The structure of SCPPM makes direct application of the conventional turbo decoding algorithm very inefficient. Here, we describe techniques to increase the throughput and performance of a hardware SCPPM decoder. using our optimizations, we demonstrate a 6 mega-bits per second (Mbps) decoder realization on a single FPGA. Extension toa higher data rate decoder using multiple FPGAs is readily achievable. Similar codes designed for the optical channel can benefit from our optimization techniques.
Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.