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In communication theory, the conventional role of precoding is to reshape a spectrally flat sequence of data symbols in favor of a particular inter-symbol interference (ISI) channel such that signal-to-noise power ratio (SNR) is maximized. In contrast, in this paper a novel precoding technique is devised to exploit a particular property of the information source rather than the channel. Specifically, we focus on the scenario where the source sequence has an inherent correlation that is known a priori, and design a precoding filter that attempts to reduce the average power of the resulting transmit symbol sequences. The proposed precoding technique is thus termed power-reductive precoding (PRP). This reduction of average transmit power accrues without changing the amplitude of the original sequence and thus can be treated as a system gain. An apparent drawback of this approach is the intentional ISI introduced by the precoding filter, which may lessen the minimum distance among legitimate sequences. Nevertheless, we show that even if the loss associated with the minimum distance penalty is properly taken into account, the achievable error rate versus SNR can be made superior to the case without precoding.