  This paper introduces a novel technique that enables access by a cognitive
secondary user (SU) to a spectrum occupied by an incumbent primary user (PU)
that employs Type-I Hybrid ARQ. The technique allows the SU to perform
selective retransmissions of SU data packets that have not been successfully
decoded in the previous attempts. The temporal redundancy introduced by the PU
ARQ protocol and by the selective retransmission process of the SU can be
exploited by the SU receiver to perform interference cancellation (IC) over
multiple transmission slots, thus creating a "clean" channel for the decoding
of the concurrent SU or PU packets. The chain decoding technique is initiated
by a successful decoding operation of a SU or PU packet and proceeds by an
iterative application of IC in order to decode the buffered signals that
represent packets that could not be decoded before. Based on this scheme, an
optimal policy is designed that maximizes the SU throughput under a constraint
on the average long-term PU performance. The optimality of the chain decoding
protocol is proved, which determines which packet the SU should send at a given
time. Moreover, a decoupling principle is proved, which establishes the
optimality of decoupling the secondary access strategy from the chain decoding
protocol. Specifically, first, the SU access policy, optimized via dynamic
programming, specifies whether the SU should access the channel or not, based
on a compact state representation of the protocol; and second, the chain
decoding protocol embeds four basic rules that are used to determine which
packet should be transmitted by the SU. Chain decoding provably yields the
maximum improvement that can be achieved by any scheme under our assumptions,
and thus it is the ultimate scheme, which completely closes the gap between
previous schemes and optimality.
