Canonical conditions for K/2 degrees of freedom


Recep Gül, David Stotz, Syed Ali Jafar, Helmut Bölcskei, and Shlomo Shamai (Shitz)


IEEE Transactions on Information Theory, Vol. 68, No. 3, pp. 1716-1730, Mar. 2022.

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We present a condition for 1/2 degree of freedom for each user in constant K-user single-antenna interference channels. This condition is sufficient for all and necessary for almost all channel matrices. Moreover, it applies to all channel topologies, i.e., to fully-connected channels as well as channels that have individual links absent, reflected by corresponding zeros in the channel matrix. Moreover, it captures the essence of interference alignment by virtue of being expressed in terms of a generic injectivity condition that guarantees separability of signal and interference. Finally, we provide codebook constructions achieving 1/2 degree of freedom for each user for all channel matrices satisfying the condition we identified.


Interference channels, degrees of freedom, self-similar distributions, additive combinatorics, Rényi information dimension

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