Chapter 14: Space-Time Coding for ARQ

Learning Objectives

• Describe the ARQ protocol as a sequence of up to $L$ transmission rounds over independent block-fading MIMO realisations, distinguish Chase combining (CC) from incremental redundancy (IR), and explain why IR strictly dominates CC in the diversity-multiplexing-delay sense
• State the El Gamal-Caire-Damen ARQ-DMT theorem: on an $n_t \times n_r$ i.i.d. Rayleigh channel with at most $L$ ARQ rounds, the optimal tradeoff curve is $d_{\mathrm{ARQ}}(r, L) = L \cdot d^{*}(r/L)$, where $d^{*}(\cdot)$ is the Zheng-Tse static DMT of Chapter 12
• Prove achievability of the ARQ-DMT via incremental-redundancy random Gaussian codes, and prove the converse via an outage bound on the $L$-round mutual information
• Define incremental-redundancy lattice space-time (IR-LAST) codes as nested CDA-based constructions, and explain why they achieve the ARQ-DMT at every $(r, L)$
• Map the ARQ-DMT story onto practical HARQ in LTE and 5G NR: redundancy versions, circular-buffer rate matching, stop-and-wait parallel HARQ processes, and URLLC retransmission budgets
• Reason quantitatively about the operational cost of ARQ — latency, feedback overhead, independence assumption on successive rounds — and when the ARQ-DMT prediction of $L$-fold diversity gain fails to materialise in practice