  The use of open-loop coding can be easily extended to a closed-loop
concatenated code if the channel has access to feedback. This can be done by
introducing a feedback transmission scheme as an inner code. In this paper,
this process is investigated for the case when a linear feedback scheme is
implemented as an inner code and, in particular, over an additive white
Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive
the optimal linear feedback scheme by optimizing over the received
signal-to-noise ratio. From this optimization, an asymptotically optimal linear
feedback scheme is produced and compared to other well-known schemes. Then, the
linear feedback scheme is implemented as an inner code to a concatenated code
over the AWGN channel with noisy feedback. This code shows improvements not
only in error exponent bounds, but also in bit-error-rate and frame-error-rate.
It is also shown that the if the concatenated code has total blocklength L and
the inner code has blocklength, N, the inner code blocklength should scale as N
= O(C/R), where C is the capacity of the channel and R is the rate of the outer
code. Simulations with low density parity check (LDPC) and turbo codes are
provided to display these advantages.
