Explicit Performance Bound of Finite Blocklength Coded MIMO: Time-Domain versus Spatiotemporal Channel Coding

TL;DR

The paper derives explicit finite-blocklength performance bounds for MIMO systems under two coding paradigms: spatiotemporal coding and time-domain coding. Using achievability and converse bounds together with normal approximation, it shows that spatiotemporal coding can offset short blocklength penalties by increasing spatial DoF, while time-domain coding cannot. The key results include closed-form expressions for the per-channel-use capacity and dispersion under each mode and their ergodic refinements, highlighting a fundamental advantage of spatiotemporal coding in URLLC regimes. This work provides a theoretical foundation for designing practical spatiotemporal codes to achieve extreme connectivity in 6G.

Abstract

In the sixth generation (6G), ultra-reliable low-latency communications (URLLC) will be further developed to achieve TKu extreme connectivity. On the premise of ensuring the same rate and reliability, the spatial domain advantage of multiple-input multiple-output (MIMO) has the potential to further shorten the time-domain code length and is expected to be a key enabler for the realization of TKu. Different coded MIMO schemes exhibit disparities in exploiting the spatial domain characteristics, so we consider two extreme MIMO coding schemes, namely, time-domain coding in which the codewords on multiple spatial channels are independent of each other, and spatiotemporal coding in which multiple spatial channels are jointly coded. By analyzing the statistical characteristics of information density and utilizing the normal approximation, we provide explicit performance bounds for finite blocklength coded MIMO under time-domain coding and spatiotemporal coding. It is found that, different from the phenomenon in time-domain coding where the performance declines as the blocklengths decrease, spatiotemporal coding can effectively compensate for the performance loss caused by short blocklengths by improving the spatial degrees of freedom (DoF). These results indicate that spatiotemporal coding can optimally exploit the spatial dimension advantages of MIMO systems, enabling extremely low error-rate communication under stringent blocklengths constraint.

Figures (6)

• Figure 1: Different block diagrams of MIMO transmitting systems using spatiotemporal coding and time-domain coding.
• Figure 2: Comparison of the achievability and converse bounds with the normal approximation in spatiotemporal coding with $\varepsilon=10^{-7}$.
• Figure 3: The fitting results of the expectation of channel dispersion under different coding modes with $\rho = 10 \text{ dB}$.
• Figure 4: The fitting results of the average maximal achievable rate per link under different coding modes with fixed proportion of transceiver antennas $c=L/N=16$, $n=100$ and $\varepsilon={10}^{-7}$.
• Figure 5: The relationship between the average maximal achievable rate per link and Shannon capacity under different coding modes with $\rho = 10 \text{ dB}$ and $\varepsilon={10}^{-7}$.

Theorems & Definitions (14)

• Lemma 1: polyanskiy2010channel
• Lemma 2: mann1996berry, Berry-Esseen central-limit theorem (CLT)
• Lemma 3: polyanskiy2010channel, Theorem 25
• Lemma 4: polyanskiy2010channel, Theorem 31
• Lemma 5: collins2016dispersion, Proposition 3
• Remark 1
• Proposition 1
• Lemma 6: collins2018coherent, Lemma 18
• Theorem 1
• Proposition 2