ABSTRACT

This project develops the theoretical framework necessary to achieve, on certain data communication channels, the highest possible reliable data rate while still using low-complexity practical decoders. Applications include satellites communicating using either free-space optical communication or radio-frequency communication. Practically all data is communicated by sending a sequence of symbols transmitted as a waveform over a physical channel. These symbols often determine the amplitudes and/or phases of the waveform and are typically drawn from a discrete alphabet of possible values. Traditionally, symbol alphabets are symmetric. For example, if there is a symbol with an amplitude of +5 volts there will also be a symbol with an amplitude of -5 volts. For symmetric alphabets, there are a variety of existing coded modulation techniques that achieve high data rates using practical decoders. However, for important channels including common satellite channels, the best alphabets turn out not to be symmetric. This significantly complicates the design both of the coded modulation to achieve the highest rates and of the associated decoding algorithms. This project develops techniques that identify the optimal placement of alphabet symbols without requiring symmetry and introduces a new form of coded modulation, known as probabilistic permutation shaping, that achieves the highest possible data rates while still allowing practical decoders to use the optimal asymmetric alphabets. The practical impact from a successful outcome of this research will lead to high-speed satellite links for both earth-space and vice-versa.

This project utilizes probabilistic permutation shaping, which approaches channel capacity using a practical low-density parity check (LDPC) decoder even when the optimal input distribution is asymmetric. This approach avoids the complexity and error propagation of multi-layer coding with multi-stage decoding. It also avoids the latency and performance loss associated with joint de-mapping and decoding. The project also develops a family of new optimization techniques utilizing a modification of the Blahut-Arimoto algorithm that dynamically re-assigns the positions of mass points. Dynamic-assignment Blahut-Arimoto characterizes not only point solutions at a specific signal-to-noise ratio, but the entire evolution of the minimal cardinality optimal finite-support distributions as the channel capacity increases over the entire range of interest. In the context of these families of finite-support distributions, which are inherently asymmetric, probabilistic permutation shaping builds on the existing framework of probabilistic amplitude shaping to provide flexible and practical coded modulation solutions that support entire families of non-uniform distributions that would have previously been considered exotic.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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