PEG Encoding Algorithm for LDPC Codes

In this article, we provide a detailed discussion of LDPC codes and the PEG (Progressive Edge-Growth) encoding algorithm. First, we introduce the fundamental concepts of LDPC codes, covering their structural properties, key characteristics, and practical applications in communication systems. Subsequently, we conduct an in-depth exploration of the PEG encoding algorithm, explaining its operational principles, advantages in generating high-girth Tanner graphs, and limitations regarding code performance optimization. The algorithm implementation typically involves iterative edge placement strategies that maximize local girth during graph construction. Furthermore, we examine the application of PEG algorithm in LDPC code construction and demonstrate practical implementation approaches using matrix manipulation techniques and graph theory algorithms. Through systematic exposition of these concepts, readers will gain comprehensive understanding of LDPC codes and PEG encoding algorithm, enabling effective application in practical coding scenarios including parameter configuration, parity-check matrix generation, and performance evaluation metrics.