Edge-Spreading Raptor-Like LDPC Codes for 6G Wireless Systems

TL;DR

The paper addresses the need for high-throughput, energy-efficient, rate-compatible channel codes for 6G eMBB+ by introducing edge-spreading Raptor-like (ESRL) SC-LDPC codes. It develops a three-part protomatrix framework (HRC, IRC, SSC) and a tail matrix Q, and proposes a unified graph to optimally spread edges into a coupled matrix B_SC, along with a modified coupled RCA to estimate thresholds. It also provides a high-throughput SLME decoding approach and a complete design flow, including puncturing and IR-HARQ integration, and demonstrates substantial performance and throughput gains over 5G-NR LDPC in multiple scenarios. The work shows ESRL’s potential to meet next-generation demands while maintaining compatibility with existing protographs and HARQ schemes, enabling scalable, high-rate, low-latency wireless communication. The combination of unified-graph optimization, threshold analysis, and SLME decoding yields tangible improvements in error-rate performance and peak throughput for 6G wireless systems.

Abstract

Next-generation channel coding has stringent demands on throughput, energy consumption, and error rate performance while maintaining key features of 5G New Radio (NR) standard codes such as rate compatibility, which is a significant challenge. Due to excellent capacity-achieving performance, spatially-coupled low-density parity-check (SC-LDPC) codes are considered a promising candidate for next-generation channel coding. In this paper, we propose an SC-LDPC code family called edge-spreading Raptor-like (ESRL) codes. Unlike other SC-LDPC codes that adopt the structure of existing rate-compatible LDPC block codes before coupling, ESRL codes maximize the possible locations of edge placement and focus on constructing an optimal coupled matrix. Moreover, a new graph representation called the unified graph is introduced. This graph offers a global perspective on ESRL codes and identifies the optimal edge reallocation to optimize the spreading strategy. We conduct comprehensive comparisons of ESRL codes and 5G-NR LDPC codes. Simulation results demonstrate that when all decoding parameters and complexity are the same, ESRL codes have obvious advantages in error rate performance and throughput compared to 5G-NR LDPC codes in some specific scenarios (low and high number of iterations), making them a promising solution towards next-generation channel coding.

Figures (18)

• Figure 1: Comparisons of ESRL codes and 5G-NR LDPC codes 5Gstandard2016. More details are discussed in Section \ref{['sec:SecV_comp']}.
• Figure 2: Uncoupled protograph and protomatrix for an ESRL code with an HRC, an IRC, and an SSC. The upper right corner is left empty to ensure rate compatibility.
• Figure 3: The code profile of the ESRL code, including an uncoupled protomatrix $\mathbf{B}$, an edge-spreading matrix $\mathbf{T}$, and a tail matrix $\mathbf{Q}$.
• Figure 4: A unified graph $\mathcal{G}_{\text{U}}$ example, where dashed black lines and solid black lines are assigned to $\mathbf{B}_0$ and $\mathbf{B}_1$, respectively.
• Figure 5: An example of cycle counting on a unified graph $\mathcal{G}_{\text{U}}$.

Theorems & Definitions (7)

• proof
• Example 1
• Remark 1
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• Remark 2
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• proof