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.

本文研究了在加性白噪声信道上实现线性反馈编码作为内嵌编码的最佳方法，并比较了其他著名方案的性能。结果表明，该方法不仅在误码率和帧错误率上有所改善，而且在误差指数方面也有所提高。此外，模拟结果证明内嵌编码块长度应当按照 N=O (C/R) 的比例进行扩展，其中 C 为信道容量，R 为外部编码速率。