Quasi-Cyclic Low Density Parity Check

Description

Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes are a pivotal channel coding technology adopted for the 5G New Radio (NR) enhanced Mobile Broadband (eMBB) data channels. They belong to the family of LDPC codes, which are linear block codes defined by a sparse parity-check matrix (H matrix), meaning most entries are '0' and only a small fraction are '1'. The 'Quasi-Cyclic' property imposes a specific, highly regular structure on this H matrix: it is composed of smaller square sub-matrices, each of which is either a zero matrix or a cyclically shifted identity matrix (a circulant). This structure is key to its practical advantages.

The architecture of the NR QC-LDPC code is detailed in specification 38.212. The base graph is a fundamental concept. 5G NR defines two primary base graphs (BG1 and BG2). BG1 is larger and designed for larger transport blocks and higher code rates, offering the best peak throughput. BG2 is smaller, optimized for smaller transport blocks and lower code rates, providing better performance for edge-of-cell conditions and small data packets. The encoding process involves expanding these base graphs by a lifting factor 'Z', which determines the size of the circulant sub-matrices. This creates the final parity-check matrix for a specific block size and code rate. The decoder, typically an iterative belief propagation algorithm, exchanges probabilistic messages (soft information) between variable nodes and check nodes represented in the code's Tanner graph, which is directly derived from the H matrix.

QC-LDPC's role in the 5G NR physical layer is to protect user and control data from errors introduced during transmission over the radio channel. It is used for the Physical Downlink Shared Channel (PDSCH) and Physical Uplink Shared Channel (PUSCH). Its structured quasi-cyclic nature enables highly efficient parallel processing in both encoder and decoder hardware implementations. This parallelism is crucial for meeting 5G's extreme throughput requirements (multi-gigabit speeds) and low-latency targets, as it allows multiple bits to be processed simultaneously. The performance of QC-LDPC is characterized by a very steep 'waterfall' region in its bit error rate curve, meaning that once the signal-to-noise ratio passes a certain threshold, the error rate drops dramatically, enabling reliable communication at rates very close to the channel capacity.

Purpose & Motivation

QC-LDPC was introduced to overcome the limitations of the Turbo codes used in 4G LTE for data channels. While Turbo codes were a major advancement for 3G and 4G, they faced challenges in the 5G context. For very high data rates (multi-Gbps), Turbo code decoder implementations suffered from high implementation complexity, longer latency due to their iterative serial nature, and a perceived performance ceiling. Furthermore, Turbo codes exhibited an 'error floor' at very low error rates, which was problematic for ultra-reliable communications.

The primary problems QC-LDPC solves are the need for higher throughput, lower latency, and more flexible channel coding for 5G's diverse use cases. Its structured design allows for massive parallelization in decoder architectures, directly addressing the throughput bottleneck. The parallelizable decoding algorithm also reduces processing latency compared to the more serialized Turbo decoding. The use of two base graphs provides inherent flexibility, allowing the system to efficiently code transport blocks ranging from very small (e.g., for IoT) to extremely large (e.g., for eMBB) without the significant padding overhead required by LTE's Turbo code. The selection of QC-LDPC was the result of extensive evaluation and was motivated by its superior performance at the high code rates prevalent in 5G, its suitability for hardware implementation, and its lack of a high error floor.

Key Features

• Parity-check matrix built from circulant permutation matrices, enabling efficient parallel processing
• Two base graphs (BG1 and BG2) to cover a wide range of block sizes and code rates optimally
• Supports incremental redundancy Hybrid ARQ (HARQ) through flexible rate matching
• Exhibits a steep waterfall performance curve and very low error floor
• Enables high-throughput, low-latency decoder implementations essential for 5G peak data rates
• Adopted as the mandatory channel code for 5G NR eMBB data channels (PDSCH/PUSCH)

Evolution Across Releases

Defining Specifications