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Study on Decoding Algorithm for Non-Binary LDPC Codes

Lei Wen

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Abstract

Non-binary LDPC codes are obtained by generalizing binary LDPC coeds from finite field GF(2) to finite field GF(q).Its elements of parity check matrix are not(0,1),but ensemble(0,1,…,q-1),and its decoding method still employs belief propagation and iterative algorithm.This paper mainly derives the iterative formulas of decoding algorithm for Non-Binary LDPC codes and analyzes an improved algorithm based on FFT.Finally,the predominant performance of FFT decoding algorithm is verified by simulation.

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What this paper is about

Non-binary LDPC codes are obtained by generalizing binary LDPC coeds from finite field GF(2) to finite field GF(q).Its elements of parity check matrix are not(0,1),but ensemble(0,1,…,q-1),and its decoding method still employs belief propagation and iterative algorithm.This paper mainly derives the iterative formulas of decoding algorithm for Non-Binary LDPC codes and analyzes an improved algorithm based on FFT.Finally,the predominant performance of FFT decoding algorithm is verified by simulation.

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Available abstract

Non-binary LDPC codes are obtained by generalizing binary LDPC coeds from finite field GF(2) to finite field GF(q).Its elements of parity check matrix are not(0,1),but ensemble(0,1,…,q-1),and its decoding method still employs belief propagation and iterative algorithm.This paper mainly derives the iterative formulas of decoding algorithm for Non-Binary LDPC codes and analyzes an improved algorithm based on FFT.Finally,the predominant performance of FFT decoding algorithm is verified by simulation.

Key concepts: Low-density parity-check code, Berlekamp–Welch algorithm, Computer science, Algorithm, Decoding methods, Belief propagation, Fast Fourier transform, Binary number

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