On Decoding Fountain Codes with Erroneous Received Symbols
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Motivated by the application of fountain codes in the DNA-based data storage systems, in this paper, we consider the decoding of fountain codes when the received symbols have a chance to be incorrect. Unlike the conventional scenario where the received symbols are all error-free, the maximum likelihood (ML) decoding and maximum a posterior probability (MAP) decoding are not practical under this situation due to the exponentially high complexity. Instead, we propose an efficient algorithm, which is referred to as the basis-finding algorithm (BFA) for decoding. We develop a straightforward implementation as well as an efficient implementation for the BFA, both of which have polynomial time complexities. Moreover, to investigate the frame error rate (FER) of the BFA, we derive the theoretical bounds and also perform extensive simulations. Both the analytical and simulation results reveal that the BFA can perform very well for decoding fountain codes with erroneous received symbols.
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