Network modulation: Simultaneous optimality in multi-user communication
Yuval Kochman MIT
Abstract: The choice of modulation domain plays a major role in communications, both in deriving performance limits and in the design of practical schemes which decouple the signal processing task of channel equalization from coding. Thus, choosing the “right” basis is of central importance. For example, the capacity of the Gaussian inter- symbol interference (ISI) channel is given by the water-filling solution, applied in the frequency domain; the same transformation also allows to use popular schemes such as Orthogonal Frequency-Division Multiplexing (OFDM) which employs the discrete Fourier transform. The singular-value decomposition (SVD) plays a similar role for multiple-input multiple-output (MIMO) channels. Common to both cases is diagonalization: they yield parallel independent equivalent channels. But do we really need such orthogonality? Capacity can be achieved for both the ISI and MIMO channels using non-orthogonal equivalent channels, by a receiver which performs triagularlization of the channel (rather than diagonalization) and then decision-feedback equalization or successive interference cancellation (SIC). This is done without performing any transformation at the encoder. It is therefore natural to ask, what can be achieved by allowing (in addition to linear processing at the receiver) both an encoder transformation (linear unitary processing) and SIC.
In this work we show that in various communication scenarios, such a combination is indeed advantageous. In particular, the degrees of freedom earned by allowing SIC may be used for obtaining a domain which is simultaneously optimal for two users. We demonstrate this advantage by applying the network modulation approach to several problems. For some cases of joint source-channel coding over MIMO broadcast channels, we are able to derive the optimal distortion region by applying a hybrid digital-analog scheme over the equivalent triangular channels. For the two-way MIMO relay channel we find the capacity in the high signal-to-noise ratio limit by using physical- layer modulo-lattice arithmetic over these equivalent channels. For the Gaussian common-message MIMO broadcast channel, as well as for Gaussian rateless coding, we get schemes which allow to achieve the known optimal performance using standard scalar codes.
Joint work with Anatoly Khina, Uri Erez and Gregory W. Wornell.
Yuval Kochman received his B.Sc., M.Sc. and Ph.D. degrees from Tel Aviv University in 1993, 2003 and 2010, respectively, all in electrical engineering. He is a postdoctoral associate at the at the Signals, Information and Algorithms Laboratory at the Massachusetts Institute of Technology (MIT), since 2009. Outside academia, he has worked in the areas of radar and digital communications. His research interests include information theory, communications and signal processing.
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