Several modulation and coding advances supported by NASA are summarized. To support long-constraint-length convolutional code, a VLSI maximum-likelihood decoder, utilizing parallel processing techniques, which is being developed to decode convolutional codes of constraint length 15 and a code rate as low as 1/6 is discussed. A VLSI high-speed 8-b Reed-Solomon decoder which is being developed for advanced tracking and data relay satellite (ATDRS) applications is discussed. A 300-Mb/s modem with continuous phase modulation (CPM) and codings which is being developed for ATDRS is discussed. Trellis-coded modulation (TCM) techniques are discussed for satellite-based mobile communication applications.>

Traditionally symmetric signal constellations, i.e., those with uniformly spaced signal points, have been used for both uncoded and coded systems. Although symmetric signal constellations are optimum with no coding, the same is not necessarily true for coded systems. This paper shows that by designing the signal constellations to be asymmetric, one can, in many instances, obtain a performance gain over the traditional symmetric constellations combined With trellis coding. In particular, we consider the joint design ofn/(n + 1)trellis codes and asymmetric2^{n+1}-point signal constellations, which has no bandwidth expansion relative to an uncoded 2n-point symmetric signal set. The asymptotic performance gains due to coding and asymmetry are evaluated in terms of the minimum free Euclidean distance dfreeof the trellis. A comparison of the maximum value of this performance measure to the minimum distance dmin, of the uncoded system is an indication of the maxiamm reduction in requiredE_{b}/N_{0}that can be achieved for arbitrarily small system bit error rates. Bit error probability analysis is carried out for general cases. A few examples are given to show the performance gain due to the asymmetry of the signal set. It is to be emphasized that the introduction of asymmetry into the signal set does not affect the bandwidth or power requirements of the system; hence, the abovementioned improvements in performance come at little or no cost. Asymmetric signal sets in coded systems first appear in the work of Divsalar and Yuen [1], [2]. Here we expand upon these results by considering various types of asymmetric signal sets combined with the optimum (in the sense of maximum dfree) trellis code having 2, 4, 8, and 16 states. The numerical results obtained will clearly demonstrate the tradeoff between the additional savings in requiredE_{b}/N_{0}and the additional complexity (more trellis states) needed to achieve it.

A pipeline structure of a transform decoder similar to a systolic array is developed to decode Reed-Solomon (RS) codes. The error locator polynomial is computed by a modified Euclid's algorithm which avoids computing inverse field elements. The new decoder is regular and simple, and naturally suitable for VLSI implementation.

A pipeline structure of a transform decoder similar to a systolic array is developed to decode Reed-Solomon (RS) codes. An important ingredient of this design is a modified Euclidean algorithm for computing the error-locator polynomial. The computation of inverse field elements is completely avoided in this modification of Euclid's algorithm. The new coder is regular and simple, and naturally suitable for VLSI implementation. An example illustrating both the pipeline and systolic array aspects of this decoder structure is given for a RS code.

Consideration is presently being given to an optical-RF relay deep space communication link that transmits optical PPM data from spacecraft to orbital relay, then retransmits the data via microwave to ground. It is generally advantageous to use Reed-Solomon (RS) encoding over the PPM optical link for improved error correction. In this paper several demodulating schemes are considered for generating the RS symbols at the relay photodetector output, and the effect of each on overall RS decoding performance is computed. Both Poisson and Gaussian optical noise models are used in the evaluation. The effect on performance of bit errors in the relay downlink is also examined.

This paper considers a system that couples several phaselocked loops (PLL's) to improve carrier tracking performance. The system coherently combines the received carrier signals at geographically separated ground antennas to increase the total effective aperture. It automatically aligns the received carrier's phases to enhance received carrier signal-to-noise ratio. The tracking performance of this system is being assessed in terms of rms phase jitter.

A nonlinear analysis which can be used to assess certain statistical characteristics of double-loop tracking systems is presented. It takes into account the mutual coupling effects of the loops in the system. Two approaches are taken to obtain steady-state probability density functions (pdf's) of the system phase errors, φ1and φ2From these pdf's, important system performance statistics, e.g., the phaseerror variances, can be calculated, thus illustrating the application and usefulness of the analysis. The analysis is applied to a satellite transponder as an example.