In this paper, we propose a framework to attain the integrated design of polar coding and spatial modulation (SM) such that the performance of coded SM-MIMO system can be efficiently improved. This Polar-SM framework recognizes SM and polar coding from a unified perspective of polarization by which the original SM-MIMO channel is split into a series of bit polarized subchannels under the three-stage channel transform, i.e., index-symbol $\to$ modulation $\to$ bit partitions. This paradigm exploits the underlying weak polarization effect within the SM signal, then concatenates with the binary polarization in polar coding, forming a signal-coding cascaded polarization framework. In particular, the first stage channel transform serially decomposes the original SM-MIMO channel into the index subchannel and the symbol subchannel. This mechanism follows the chain rule of mutual information, which preserves the capacity and maximizes the polarization effect. Combining with modulation and bit partitions, we prove the capacity-achieving property of Polar-SM. From the point of practicality, we propose a rate-filling method to realize a fast and low-complexity code construction of Polar-SM. Guided by the three-stage channel transform, we design a glued successive cancellation list (gSCL) decoding algorithm at the receiver to integrate SM detection and polar decoding as a collaborative ensemble. Simulation results validate the performance gain of Polar-SM over state-of-the-art polar-coded MIMO systems and LDPC-coded SM systems.

中文翻译：

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极性编码的空间调制

在本文中，我们提出了一个框架来实现极性编码和空间调制（SM）的集成设计，从而可以有效地提高已编码SM-MIMO系统的性能。这个Polar-SM框架从统一的极化角度识别SM和极化编码，在三阶段信道变换（即索引符号）下，原始SM-MIMO信道将极化SM分为多个比特极化子信道 $ \至$ 调制 $ \至$ 位分区。这种范例利用了SM信号中潜在的弱极化效应，然后在极性编码中与二进制极化相串联，从而形成了信号编码级联极化框架。特别地，第一级信道变换将原始SM-MIMO信道串行分解为索引子信道和符号子信道。该机制遵循互信息的链式规则，从而保留了容量并最大化了极化效应。结合调制和位分割，我们证明了Polar-SM的容量实现特性。从实用性的角度出发，我们提出了一种速率填充方法，以实现Polar-SM的快速且低复杂度的代码构造。在三阶段通道转换的指导下，我们在接收器处设计了一种粘连的连续消除列表（gSCL）解码算法，以将SM检测和极地解码集成为一个协作集合。仿真结果验证了Polar-SM在最新的极性编码MIMO系统和LDPC编码SM系统上的性能增益。