On the Capacity of Symmetric M-user Gaussian Interference Channels with Feedback
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A general time-varying feedback coding scheme is proposed for M-user fully connected symmetric Gaussian interference channels. Based on the analysis of the general coding scheme, we prove a theorem which gives a criterion for designing good time-varying feedback codes for Gaussian interference channels. The proposed scheme improves the Suh-Tse and Kramer inner bounds of the channel capacity for the cases of weak and not very strong interference when M=2. This capacity improvement is more significant when the signal-to-noise ratio (SNR) is not very high. In addition, our coding scheme can be proved mathematically and numerically to outperform the Kramer code for M≥ 2 when Signal to Noise Ratio (SNR) is equal to Interference to Noise Ratio (INR). Besides, the generalized degrees-of-freedom (GDoF) of our proposed coding scheme can be proved to be optimal in the all network situations (very weak, weak, strong, very strong) for any M. The numerical results show that our coding scheme can attain better performance than the Suh-Tse coding scheme for M=2 or the Mohajer-Tandon-Poor lattice coding scheme for M>2. Furthermore, the simplicity of the encoding/decoding algorithms is another strong point of our proposed coding scheme compared with the Suh-Tse coding scheme when M=2 and the Mohajer-Tandon-Poor lattice coding scheme when M>2. More importantly, our results show that an optimal coding scheme for the symmetric Gaussian interference channels with feedback can be achieved by only using marginal posterior distributions under a better cooperation strategy between transmitters.
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