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However, this property may fail to hold in point-to-point communications if the source is non-ergodic, the channel is time-varying, the system is delay or complexity constrained, or when we are dealing with a network scenario.

In this case, there are potential benefits to be gained by looking at the problem from a joint source-channel coding perspective rather than the two narrower perspectives of source and channel coding. Another result, again due to Shannon, shows that the presence of a noiseless feedback link from the output of the channel to the encoder does not increase the capacity of point-to-point memoryless channels. However the presence of a feedback link can help in decreasing the complexity of implementation as well as the delay associated with the system.

In this thesis, we combine these two ideas to look at the problem of feedback communications from a joint source-channel coding perspective. We first outline a joint source-channel coding scheme and show rigorously that the expected number of channel uses to decode each source symbols approaches the source entropy divided by the channel capacity.

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Multiple-repetition coding for channels with feedback

This is a block decoding strategy and the complexity of this scheme is exponential in the block length. However, the system is optimal in the sense that no other scheme can decode source symbols with a lower number of channel uses on the average.

We next focus on a modified low-complexity variant of the scheme considered earlier. This low-complexity implementation has a number of desirable properties. First, the source symbols are decoded one by one. The delay per source symbol is essentially a constant.

A Coding Scheme for Colored Gaussian Wiretap Channels with Feedback

Secondly, simulation results show that the symbol errors are confined locally and do not propagate. Thirdly, the scheme can adaptively learn the parameters of interest and approach optimal performance. Finally, the presence of a high capacity feedback link makes the structure of the encoder extremely simple.


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In this paper, the finite-order autoregressive moving average ARMA Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper.

Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback channel. Furthermore, the results are extended to the additive white Gaussian noise AWGN channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate.

HY Information and Coding Theory – Department of Electrical and Computer Engineering

As the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel. Vincent ; Shamai, Shlomo.

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N2 - In this paper, the finite-order autoregressive moving average ARMA Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. AB - In this paper, the finite-order autoregressive moving average ARMA Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels.