This work identifies the fundamental limits of cache-aided coded multicasting in the presence of the well-known worst-user' bottleneck. This stems from the presence of receiving users with uneven channel capacities, which often forces the rate of transmission of each multicasting message to be reduced to that of the slowest user. This bottleneck, which can be detrimental in general wireless broadcast settings, motivates the analysis of coded caching over a standard Single-Input-Single-Output (SISO) Broadcast Channel (BC) with K cache-aided receivers, each with a generally different channel capacity. For this setting, we design a communication algorithm that is based on superposition coding that capitalizes on the realization that the user with the worst channel may not be the real bottleneck of communication. We then proceed to provide a converse that shows the algorithm to be near optimal, identifying the fundamental limits of this setting within a multiplicative factor of 4. Interestingly, the result reveals that, even if several users are experiencing channels with reduced capacity, the system can achieve the same optimal delivery time that would be achievable if all users enjoyed maximal capacity.
Our work is in the spirit of all the above papers, and it can be seen specifically as an extension of @cite_20 . This reference considered a specific binary topological case, for which it proposed a two-level superposition-based transmission scheme to alleviate the worst-user bottleneck.
@cite_20
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We explore the performance of coded caching in a SISO BC setting where some users have higher link capacities than others. Focusing on a binary and fixed topological model where strong links have a fixed normalized capacity 1, and where weak links have reduced normalized capacity T < 1, we identify — as a function of the cache size and T — the optimal throughput performance, within a factor of at most 8. The transmission scheme that achieves this performance, employs a simple form of interference enhancement, and exploits the property that weak links attenuate interference, thus allowing for multicasting rates to remain high even when involving weak users. This approach ameliorates the negative effects of uneven topology in multicasting, now allowing all users to achieve the optimal performance associated to T = 1, even if τ is approximately as low as T ≥ 1 − (1 − w)g where g is the coded-caching gain, and where w is the fraction of users that are weak. This leads to the interesting conclusion that for coded multicasting, the weak users need not bring down the performance of all users, but on the contrary to a certain extent, the strong users can lift the performance of the weak users without any penalties on their own performance. Furthermore for smaller ranges of τ, we also see that achieving the near-optimal performance comes with the advantage that the strong users do not suffer any additional delays compared to the case where T = 1.