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Also known as: Low-Density Parity-Check, Gallager Code
Sparse parity-check codes decoded iteratively with message passing, achieving near-capacity performance on many channels.
DESCRIPTION
LDPC codes are linear block codes characterized by sparse parity-check matrices and graph-based decoding. Iterative algorithms like belief propagation exchange messages on Tanner graphs to converge to likely codewords. Modern standards (DVB-S2, Wi-Fi, 5G NR) adopt LDPC for high throughput and reliability. Their performance approaches Shannon limits with manageable complexity for long block lengths. Code design involves degree distributions, girth, and spatial coupling to avoid error floors. Hardware and software implementations leverage parallelism inherent in message passing.
ALTERNATIVE DEFINITIONS
Wikipedia
In information theory, a low-density parity-check (LDPC) code is a linear error-correcting code with a parity-check matrix that contains only a small number of nonzero elements.
Defines LDPC by sparsity of the parity-check matrix.
Wolfram MathWorld
An LDPC code is a linear error-correcting code defined by a sparse parity-check matrix and typically decoded by iterative message-passing algorithms.
Emphasizes decoding via message passing on sparse graphs.
RELATED TERMS
Parity-Check Matrix Tanner Graph Belief Propagation Error-Correcting Code 3GPP 5G NR DVB-S2 Sparse Matrix Generator Matrix Iterative Decoding
COMPETING TERMS
KNOWLEDGE AREAS
Infrastructure IoT & Edge Data Real-time & Streaming Data Mathematics
TARGET AUDIENCE
Hardware Engineer Software Developer Data Engineer
EXTERNAL SOURCES
- Wikipedia - Low-density parity-check code
- ETSI - DVB-S2 physical layer with LDPC
- 3GPP - 5G NR channel coding (LDPC)
- arXiv - Survey on LDPC codes and decoding
TOP QUESTIONS
Why are LDPC Codes widely used in modern standards?
They deliver near-capacity performance with scalable, parallelizable decoding suitable for high-throughput systems like DVB-S2 and 5G NR.
Category: Relevancy
How does LDPC decoding work?
Iterative message passing updates beliefs on a Tanner graph until convergence or a maximum number of iterations.
Category: HowTo
What is a Tanner graph in LDPC Codes?
A bipartite graph connecting variable and check nodes that represents the parity-check constraints of the code.
Category: Concept
What causes error floors in LDPC Codes?
Short cycles and trapping sets in the graph can hinder convergence, producing elevated residual error rates.
Category: Risks
How do spatially coupled LDPC Codes improve performance?
Coupling enhances iterative decoding thresholds, enabling performance closer to capacity and mitigating error floors.
Category: Topic
How do LDPC Codes compare to Turbo Codes?
LDPC often outperform at high throughputs and long blocks; Turbo codes can be competitive at moderate lengths and lower complexity.
Category: Comparison
What design choices matter for LDPC Codes?
Degree distributions, girth, lifting schemes, and base graph selection critically impact performance and complexity.
Category: Requirements
What implementations exist for LDPC decoding?
Hardware accelerators and SIMD-parallel software implement sum-product or min-sum variants with early-stopping heuristics.
Category: Example
How do you evaluate LDPC performance?
Simulate BER/FER vs. SNR curves, analyze waterfall and error floor regions, and measure throughput and latency.
Category: HowTo