Resolving the Feedback Bottleneck of Multi-Antenna Coded Caching

Abstract

Multi-antenna cache-aided wireless networks were thought to suffer from a severe feedback bottleneck, since achieving the maximal Degrees-of-Freedom (DoF) performance required feedback from all served users for the known transmission schemes. These feedback costs match the caching gains and thus scale with the number of users. In the context of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> -antenna Multiple-Input Single Output broadcast channel with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> receivers, each having normalized cache size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> , we pair a fundamentally novel algorithm together with a new information-theoretic converse and identify the optimal tradeoff between feedback costs and DoF performance, by showing that having channel state information from only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C&lt; L$ </tex-math></inline-formula> served users implies an optimal one-shot linear DoF of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C+K\gamma $ </tex-math></inline-formula> . As a side consequence of this, we also now understand that the well known DoF performance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L+K\gamma $ </tex-math></inline-formula> is in fact exactly optimal. In practice, the above means that we are able to disentangle caching gains from feedback costs, thus achieving unbounded caching gains at the mere feedback cost of the multiplexing gain. This further solidifies the role of caching in boosting multi-antenna systems; caching now can provide unbounded DoF gains over multi-antenna downlink systems, at no additional feedback costs. The above results are extended to also include the corresponding multiple transmitter scenario with caches at both ends.