  This paper studies the noncausal relay channel, also known as the relay
channel with unlimited lookahead, introduced by El Gamal, Hassanpour, and
Mammen. Unlike the standard relay channel model, where the relay encodes its
signal based on the previous received output symbols, the relay in the
noncausal relay channel encodes its signal as a function of the entire received
sequence. In the existing coding schemes, the relay uses this noncausal
information solely to recover the transmitted message and then cooperates with
the sender to communicate this message to the receiver. However, it is shown in
this paper that by applying the Gelfand--Pinsker coding scheme, the relay can
take further advantage of the noncausally available information, which can
achieve strictly higher rates than existing coding schemes. This paper also
provides a new upper bound on the capacity of the noncausal relay that strictly
improves upon the cutset bound. These new lower and upper bounds on the
capacity coincide for the class of degraded noncausal relay channels and
establish the capacity for this class.
