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In this paper, we develop achievability schemes for symmetric K-user interference channels with a rate-limited feedback from each receiver to the corresponding transmitter. We study this problem under two different channel models: the linear deterministic model, and the Gaussian model. For the deterministic model, the proposed scheme achieves a symmetric rate that is the minimum of the symmetric capacity with infinite feedback, and the sum of the symmetric capacity without feedback and the symmetric amount of feedback. For the Gaussian interference channel, we use lattice codes to propose a transmission strategy that incorporates the techniques of Han-Kobayashi message splitting, interference decoding, and decode and forward. This strategy achieves a symmetric rate, which is within a constant number of bits to the minimum of the symmetric capacity with infinite feedback, and the sum of the symmetric capacity without feedback and the amount of symmetric feedback. This constant is obtained as a function of the number of users, K. We note that for the special case of Gaussian IC with K = 2, our proposed achievability scheme results in a symmetric rate that is within at most 21.085 bits/s/Hz of the outer bound, which is the first constant gap bound despite the constant gap claim in [1]. The symmetric achievable rate is used to characterize the achievable generalized degrees of freedom, which exhibits a gradual increase from no feedback to perfect feedback in the presence of feedback links with limited capacity.

On the Symmetric $K$ -User Interference Channels With Limited Feedback