In this paper, we revisit the communication problem between a single source-destination pair using a cheap relay, that is, a relay which cannot send and receive in the same frequency band simultaneously. The cheap relay channel has been considered in two forms of half-duplex relaying: time division duplex and frequency division duplex. In this paper, we show that the treatment of cheap relay channel in [9] as a channel with multiple states provides a unifying theory for both frequency division and time division relaying. Moreover, we present three non-degraded cases of the general relay channels for which the coding scheme developed in [9] is used to characterize the channel capacity. These capacity results cannot be deduced from Cover and El Gamal work on the general relay channel [1] and are the only capacity results known to date for the non-degraded discrete memoryless relay channel besides that of semi-deterministic relay channel.
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