P-Adic LDPC Codes at Precision k

In this paper, we propose the construction of p-adic LDPC codes and develop a multi-stage decoding algorithm for these codes. The novel type of non-binary error-correcting codes operates over the p-adic integers. We evaluate the error performance of these codes through simulations and compare them with existing nonbinary LDPC and Reed-Solomon codes of the same rates. Our results show that p-adic LDPC codes achieve better error performance than the existing codes. Moreover, we demonstrate the potential use of p-adic LDPC codes in byte error correction by treating each byte as an element in the p-adic integers at a chosen precision level. The p-adic LDPC codes can be designed and optimized for specific applications that require byte error correction, with the flexibility to vary the byte under different precision levels.