Chapter Summary

Chapter Summary

Key Points

• 1.

  The degraded Gaussian BC models users with heterogeneous channel qualities $\rho_1 \geq \ldots \geq \rho_K$. Each user's capacity $C_k = \log_2(1+\rho_k)$ differs, and the naive multicast rate is limited by $C_{\min} = \log_2(1+\rho_K)$ — the weakest user.

• 2.

  Naive MAN over BC achieves per-user throughput $C_{\min}(1 + t)/(1 - \mu)$, bottlenecked by the weakest user's capacity. Better schemes use superposition coding or user grouping to exploit channel heterogeneity.

• 3.

  The JLEC 2019 separation theorem characterizes the GDoF region for mixed cacheable/uncacheable traffic on a cache-aided BC: the GDoF tradeoff is a pentagon-like region with boundary $\mathrm{GDoF}_c/(t+L) + \mathrm{GDoF}_u/L \leq K$. The optimal scheme is time-sharing between pure-cacheable Lampiris-Caire mode and pure-uncacheable MU-MIMO mode.

• 4.

  Cacheable traffic benefits from both mechanisms: $\mathrm{DoF}_c = t + L$ under Lampiris-Caire (Ch 5). Uncacheable traffic benefits only from spatial multiplexing: $\mathrm{DoF}_u = L$ via pure MU-MIMO. Caches cannot substitute for traffic unknown at placement time.

• 5.

  Separation is GDoF-optimal. No joint coding scheme achieves strictly more in the GDoF regime. This is a clean information-theoretic separation theorem, with operational simplicity as a bonus.

• 6.

  GDoF is an asymptotic metric. At finite SNR, pre-log constants matter and finite-SNR schemes may exploit channel correlations in ways GDoF analysis obscures. The GDoF region is an upper bound on realizable rate regions.

• 7.

  CommIT contribution (JLEC 2019): the separation theorem and its converse are the headline result. The CommIT follow-up work extends to heterogeneous cache sizes, demand privacy, and fading channels.