Low-Density Parity-Check

Description

Low-Density Parity-Check (LDPC) codes are a class of linear block codes characterized by a sparse parity-check matrix, meaning it contains mostly zeros with a low density of ones. This sparsity is fundamental to its efficient iterative decoding algorithms. In 3GPP 5G New Radio (NR), LDPC codes were selected as the primary channel coding scheme for the data channel (PDSCH and PUSCH), replacing the Turbo codes used in 4G LTE for data. The 5G NR LDPC code design is based on quasi-cyclic (QC) LDPC codes, which offer a good balance between performance and implementation efficiency. The structure is defined by a base graph (BG), of which there are two primary ones defined in the specifications: BG1 and BG2. BG1 is optimized for larger transport blocks and higher code rates, while BG2 is better suited for smaller blocks and lower rates. The encoding process involves expanding the base graph according to a lifting size (Z) to create the final parity-check matrix for a specific code block size. This structured approach allows for highly parallelized decoder implementations, which are crucial for achieving the low latency and high throughput targets of 5G. The decoder typically uses an iterative message-passing algorithm, such as the belief propagation (BP) or min-sum algorithm, which operates on a bipartite graph (Tanner graph) representation of the parity-check matrix. Nodes in this graph exchange probabilistic messages about the likelihood of bits being 0 or 1, converging on a solution over several iterations. This process provides exceptional error-correction capability, especially for the large packet sizes common in high-speed data. The performance of LDPC codes is close to the theoretical Shannon limit, making them a cornerstone technology for achieving the peak data rates and reliability required by 5G NR. Their adoption represented a significant physical layer evolution from previous generations.

Purpose & Motivation

The primary purpose of adopting LDPC codes in 5G NR was to meet the stringent data rate, latency, and reliability requirements defined for IMT-2020. The previous channel coding workhorse for data channels in 3G and 4G was the Turbo code. While revolutionary for its time, Turbo codes presented challenges for the extreme performance targets of 5G, particularly concerning throughput and decoder complexity for very large block sizes. Turbo code decoders can suffer from longer decoding latencies and implementation complexity that scales less favorably with parallelization compared to LDPC. LDPC codes, with their inherent parallelism and superior performance at large block sizes and high code rates, were identified as a more suitable candidate. The decision was also influenced by the need for energy efficiency in base stations and devices; efficient LDPC decoder architectures can reduce power consumption. Furthermore, the quasi-cyclic structure adopted by 3GPP enables efficient hardware implementation using simple shift registers and facilitates flexible rate matching through puncturing and repetition. This addresses the need for a single, versatile coding scheme that can adapt to the diverse requirements of 5G use cases, from enhanced mobile broadband (eMBB) to ultra-reliable low-latency communications (URLLC), without requiring multiple different coding schemes. The introduction of LDPC in Rel-15 was thus a fundamental physical layer innovation to future-proof the air interface.

Key Features

• Based on quasi-cyclic (QC) structure for implementation efficiency
• Uses two base graphs (BG1 and BG2) to cover a wide range of block sizes and code rates
• Supports highly parallel iterative decoding algorithms (e.g., belief propagation)
• Provides near-Shannon-limit error correction performance, especially for large blocks
• Enables flexible rate matching through puncturing, shortening, and repetition
• Fundamental for achieving multi-gigabit per second data rates in 5G NR

Evolution Across Releases

Defining Specifications