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Asia-Pacific Conference on Communications (APCC)

On the Probability of Bit Error for Binary Cyclic Codes with Bounded-Distance Decoding

Min Goo Kim, Jaehong Lee

Published Jan 1, 1993• 0 citations
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IEEE International Symposium on Information Theory (ISIT)•Jun 25, 2003•0 citations

Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes and Applications

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This paper considers the optimal generator matrices of a binary cyclic code over a binary symmetric channel with crossover probability p rarr 0 when the goal is to minimize the probability of an information bit error. A given code has many encoder realizations and the information bit error probability is a function of this realization. We derive some sufficient conditions for a binary cyclic code to have systematic optimal generator matrices under bounded distance decoding and determine many binary cyclic codes satisfying these properties.
In this paper, we propose a construction method for two-level quantum error-correcting codes via non-binary LDPC codes over an extended field of order 2p, p an integer p >; 1. The proposed quantum error-correcting codes are based on binary quasi-cyclic LDPC codes which have almost achieved a “Bounded Distance Decoding (BDD)” limit but have not surpassed the limit yet. Quantum codes constructed from the proposed method surpass the BDD limit. Furthermore the codes outperform the efficiently-decodable state-of-the-art quantum codes.