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The use of open-loop coding can be easily extended to a closed-loopconcatenated code if the channel has access to feedback. This can be done byintroducing a feedback transmission scheme as an inner code. In this paper,this process is investigated for the case when a linear feedback scheme isimplemented as an inner code and, in particular, over an additive whiteGaussian noise (AWGN) channel with noisy feedback. To begin, we look to derivethe optimal linear feedback scheme by optimizing over the receivedsignal-to-noise ratio. From this optimization, an asymptotically optimal linearfeedback scheme is produced and compared to other well-known schemes. Then, thelinear feedback scheme is implemented as an inner code to a concatenated codeover the AWGN channel with noisy feedback. This code shows improvements notonly 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 andthe 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 outercode. Simulations with low density parity check (LDPC) and turbo codes areprovided to display these advantages.

Concatenated Coding for the AWGN Channel with Noisy Feedback