Summary

Chapter Summary

Key Points

• 1.

  Finite blocklength information theory. The Polyanskiy-Poor-Verd'{u} normal approximation $R^*(n, \varepsilon) \approx C - \sqrt{V/n}\, Q^{-1}(\varepsilon)$ precisely quantifies the rate penalty for short-packet transmission. The channel dispersion $V$ is the variance of the information density and governs the $O(1/\sqrt{n})$ convergence to Shannon capacity. Halving the rate gap requires quadrupling the blocklength --- a fundamental constraint for latency-sensitive services.

• 2.

  URLLC design principles. Ultra-Reliable Low-Latency Communication requires jointly optimising reliability ($\varepsilon \leq 10^{-5}$) and latency ($\leq 1$ ms), which pull in opposite directions at short blocklength. The three main design levers are: (i) mini-slot scheduling to minimise alignment and transmission delays, (ii) diversity (frequency, spatial, multi-TRP) to steepen the error probability curve while preserving the finite-blocklength diversity order, and (iii) conservative link adaptation with reliability margins. URLLC/eMBB coexistence relies on preemption with preemption indications (PI) to limit the throughput impact on eMBB.

• 3.

  Grant-free mMTC and compressed sensing. Massive Machine-Type Communication replaces the grant-based handshake with grant-free access, where pre-assigned pilots enable joint activity detection and data recovery. The activity detection problem is a row-sparse compressed sensing problem requiring pilot length $L_p = \Omega(K_a \log(K_{\mathrm{total}}/K_a))$. Approximate Message Passing (AMP) achieves Bayes-optimal detection in the large-system limit. Multiple receive antennas at the base station reduce the required pilot overhead proportionally.

• 4.

  Unsourced random access. In the unsourced random access model, all active users share a common codebook, and the receiver outputs a list of decoded messages without user identities. The per-user probability of error (PUPE) is the natural performance metric. Coded compressed sensing schemes approach the random coding achievability bound, with the multi-user penalty scaling as $O(K_a/n)$.

• 5.

  Age of Information. AoI $\Delta(t) = t - U(t)$ measures information freshness as the time elapsed since the most recent update was generated. For the M/M/1 queue, the average AoI is $\bar{\Delta} = (1/\mu)(1 + 1/\rho + \rho^2/(1-\rho))$, minimised at a moderate utilisation $\rho^* \approx 0.53$ --- not at high throughput. This U-shaped behaviour (decreasing due to more frequent updates, then increasing due to queueing) is a universal phenomenon across queueing models. Deterministic service (M/D/1) and deterministic arrivals (D/M/1) both reduce AoI by eliminating variability.

• 6.

  Freshness vs throughput trade-off. The central lesson of this chapter is that optimising for throughput, delay, or freshness leads to different system designs. URLLC operates in a reliability-constrained regime where the finite blocklength penalty dominates. mMTC operates in a capacity-constrained regime where the number of devices is the bottleneck. AoI-optimal systems operate in a freshness-constrained regime where moderate utilisation outperforms aggressive transmission. Modern beyond-5G systems must balance all three perspectives through cross-layer optimisation.