Performance Analysis of Spatiotemporal 2-D Polar Codes for Massive MIMO With MMSE Receivers

With the evolution from 5G to 6G, ultra-reliable low-latency communication (URLLC) faces increasingly stringent performance requirements. Lower latency constraints demand shorter channel codeword length, which can severely degrade decoding performance. The massive multiple-input multiple-output (MIMO) system is considered a crucial technology to address this challenge due to its abundant spatial degrees of freedom (DoF). While polar codes are theoretically capacity-achieving in the limit of infinite codeword length, their practical applicability is limited by the latency penalty associated with the long codewords. In this paper, we establish a unified theoretical framework and propose a novel spatiotemporal two-dimensional (2-D) polar coding scheme for massive MIMO systems employing minimum mean square error (MMSE) receivers. The polar transform is jointly applied over both spatial and temporal dimensions to fully exploit the large spatial DoF. By leveraging the near-deterministic signal-to-interference-plus-noise ratio (SINR) property of MMSE detection, the spatial domain is modeled as a set of parallel Gaussian sub-channels. Within this framework, we theoretically analyze the 2-D polarization behavior based on the Gaussian approximation method and show that the proposed scheme asymptotically retains its capacity-achieving property, even under finite blocklength constraints and large spatial DoF. Simulation results further demonstrate that, compared to traditional time-domain polar codes, the proposed 2-D scheme can significantly reduce latency while guaranteeing reliability, or alternatively improve reliability under the same latency constraint—offering a capacity-achieving and latency-efficient channel coding solution for massive MIMO systems in future 6G URLLC scenarios.