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The Encoding and Decoding Principle of Q-ary LDPC Codes

Lin Wang

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Abstract

Q-ary LDPC codes is 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 uses belief propagation and iterative algorithm. This paper mainly expound the encoding and decoding principle of Q- ary LDPC codes,and introduce a Fourier transform decoding method with low complexity.We also compare the performance of Q- ary LDPC codes and RScodes,and we find that Q- ary LDPC codes will be a competitive candidate replacing RScodes forthe magnetic storage system,the future ADSL system,and the deep space communication,so it is of importantly practical value.

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What this paper is about

Q-ary LDPC codes is 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 uses belief propagation and iterative algorithm. This paper mainly expound the encoding and decoding principle of Q- ary LDPC codes,and introduce a Fourier transform decoding method with low complexity.We also compare the performance of Q- ary LDPC codes and RScodes,and we find that Q- ary LDPC codes will be a competitive candidate replacing RScodes forthe magnetic storage system,the future ADSL system,and the deep space communication,so it is of importantly practical value.

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Available abstract

Q-ary LDPC codes is 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 uses belief propagation and iterative algorithm. This paper mainly expound the encoding and decoding principle of Q- ary LDPC codes,and introduce a Fourier transform decoding method with low complexity.We also compare the performance of Q- ary LDPC codes and RScodes,and we find that Q- ary LDPC codes will be a competitive candidate replacing RScodes forthe magnetic storage system,the future ADSL system,and the deep space communication,so it is of importantly practical value.

Key concepts: Low-density parity-check code, Computer science, Decoding methods, Berlekamp–Welch algorithm, Algorithm, Finite field, Concatenated error correction code, Belief propagation

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