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Non-binary LDPC codes and their Applications

健太 笠井, Kenta Kasai

Published Aug 20, 2010• 0 citations
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In LDPC code, the structure of code's parity check matrix plays the crucial role in code performance. In this paper proposes the preliminary investigation of a designed parity check matrix from Tanner. We modify this technique in to non binary LDPC structure and decoding with FFT-SPA. We take into high code rate application more than 0.8. The result has shown that in bit error rate (BER) compare between non-binary LDPC and binary LDPC. In our results, the performance of non binary LDPC has better than binary LDPC.
We consider transmission over the binary erasure channel (BEC) using non-binary LDPC codes. We generalize the concept of stopping sets to non-binary LDPC codes. We give a combinatorial characterization of decoding failures for non-binary LDPC codes decoded via Belief Propagation (BP). Using the density evolution analysis, we compute the asymptotic residual degree distribution for non-binary LDPC codes. In order to show that asymptotically almost every code in the non-binary LDPC ensemble has a rate equal to the design rate, we generalize the arguments of Measson, Montanari, and Urbanke to the non-binary setting. This generalization enables us to compute the conditional entropy of non-binary LDPC codes. We observe that the Maxwell construction of Measson, Montanari, and Urbanke relating the performance of MAP and BP decoding, holds in the setting of non-binary LDPC codes.