GLDPC-PC Codes for MIMO Systems with Iterative Detection and Decoding

TL;DR

This work addresses decoding latency and error floors in polar-like codes by introducing GLDPC-PC, which integrates GLDPC structure with polar-like component codes to enhance distance properties while keeping long-block performance practical. A BP-based decoder employing SO-SCL for the component polar-like decoders is developed, along with a low-complexity SISO MMSE-PIC detector for MIMO-IDD, enabling iterative exchange of extrinsic LLRs. The paper demonstrates that GLDPC-PC achieves lower error floors and competitive or superior performance in AWGN and MIMO IDD scenarios compared with 5G LDPC and polar baselines, particularly with modest iteration counts. These results suggest that GLDPC-PC is a viable, scalable option for near-capacity IDD systems in multi-antenna deployments and can be extended to other multiuser or massive MIMO contexts.

Abstract

In this work, we propose the integration of GLDPC codes with short polar-like component codes, termed GLDPC codes with polar component codes (GLDPC-PC). This approach leverages the good distance properties of polar-like codes and mitigates their high decoding latency in long block lengths. A recently proposed soft-input soft-output decoder for polar-like codes enables effective iterative belief propagation decoding for GLDPC-PC, ensuring a low error floor under additive white Gaussian noise channels. Simulation results demonstrate that GLDPC-PC codes achieve significant performance improvements in multiple-input multiple-output systems with iterative detection and decoding (IDD). The proposed GLDPC-PC codes and the IDD scheme can be applied to various scenarios.

Figures (5)

• Figure 1: The Tanner graph of $\mathbf{\Gamma}_0$ with $\tilde{n}=3$. This graph has 9 VN and 6 CN. Every VN is connected to two codes with parity check matrix $\mathbf{H}_1$ and $\mathbf{H}_2$.
• Figure 2: Transmitter and receiver scheme with iterative detection and decoding. In the receiver, the extrinsic LLR are exchanged between MIMO detector and BP decoder.
• Figure 3: BLER performance of GLDPC-PC code, 5G LDPC code and 5G polar code under AWGN channel. The block length $N$ is 1024 and message bit length $K$ is 643.
• Figure 4: BLER performance for (1024, 643) GLDPC-PC code and 5G LDPC code in $4\times 4$ MIMO channel. $N_I = R/D$ rounds of BP is performed after once detection.
• Figure 5: BLER performance for (1024, 643) GLDPC-PC code and 5G LDPC code in $8\times 8$ MIMO channel. $N_I = R/D$ rounds of BP is performed after once detection.