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Coset codes. I. Introduction and geometrical classification Export

Information Theory, IEEE Transactions on In Information Theory, IEEE Transactions on, Vol. 34, No. 5. (1988), pp. 1123-1151.

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Practically all known good constructive coding techniques for bandlimited channels, including lattice codes and various trellis-coded modulation schemes, can be characterized as coset codes. A coset code is defined by a lattice partition Λ/Λ' and by a binary encoder <e1>C</e1> that selects a sequence of cosets of the lattice Λ'. The fundamental coding gain of a coset code, as well as other important parameters such as the error coefficient, the decoding complexity, and the constellation expansion factor, are purely geometric parameters determined by <e1>C</e1> Λ/Λ'. The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters


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