Block codes on a dispersive channel

Abstract
The paper considers the effect of a dispersive channel on block codes and block coded modulation schemes. It makes use of a generalised code model which is applicable to both binary codes and more general coded modulation schemes, and a generalised channel model which models the dispersive channel in terms of its complex impulse response. This is especially applicable to the multipath and Rayleigh fading channel, but applies in general. Two types of receiver are considered, one a straightforward correlation receiver without channel equalisation, and the other a true maximum-likelihood receiver, including channel equalisation. It is shown that the auto- and crosscorrelation functions of the code sequences are important, and the implications for code design are examined. It is also shown that with channel equalisation and sufficiently large block lengths, performance degradation due to even very heavily dispersive channels is slight. Finally, three types of system are proposed, based on the results in the paper, to signal at various rates on various types of dispersive channel, giving significant advantages over the systems used at present.

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