Shannon-Kotel'nikov mappings in joint source-channel coding

Authors:
Fredrik Hekland;Pål Anders Floor;Tor A. Ramstad
Affiliations:
ABB Corporate Research Center, Billingstad, Norway;Department of Electronics and Telecommunications, Norwegian University of Science and Technology, Trondheim, Norway;Department of Electronics and Telecommunications, Norwegian University of Science and Technology, Trondheim, Norway
Venue:
IEEE Transactions on Communications
Year:
2009

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Abstract

This paper deals with lossy joint source-channel coding for transmitting memoryless sources over AWGN channels. The scheme is based on the geometrical interpretation of communication by Kotel'nikov and Shannon where amplitude-continuous, time-discrete source samples are mapped directly onto the channel using curves or planes. The source and channel spaces can have different dimensions and thereby achieving either compression or error control, depending on whether the source bandwidth is smaller or larger than the channel bandwidth. We present a general theory for 1:N and M:1 dimension changing mappings, and provide two examples for a Gaussian source and channel where we optimize both a 2:1 bandwidth-reducing and a 1:2 bandwidth-expanding mapping. Both examples show high spectral efficiency and provide both graceful degradation and improvement for imperfect channel state information at the transmitter.