Zigzag Decodable Fountain Codes

This paper proposes a fountain coding system which has lower space decoding complexity and lower decoding erasure rate than the Raptor coding systems. The main idea of the proposed fountain code is employing shift and exclusive OR to generate the output packets. This technique is known as the zigzag decodable code, which is efficiently decoded by the zigzag decoder. In other words, we propose a fountain code based on the zigzag decodable code in this paper. Moreover, we analyze the overhead for the received packets, decoding erasure rate, decoding complexity, and asymptotic overhead of the proposed fountain code. As the result, we show that the proposed fountain code outperforms the Raptor codes in terms of the overhead and decoding erasure rate. Simulation results show that the proposed fountain coding system outperforms Raptor coding system in terms of the overhead and the space decoding complexity.Comment: 11 pages, 15 figures, submitted to IEICETransactions, Oct. 201

Weight Distribution for Non-binary Cluster LDPC Code Ensemble

In this paper, we derive the average weight distributions for the irregular non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we give the exponential growth rate of the average weight distribution in the limit of large code length. We show that there exist $(2,d_c)$-regular non-binary cluster LDPC code ensembles whose normalized typical minimum distances are strictly positive.Comment: 12pages, 6 figures, To be presented in ISIT2013, Submitted to IEICE Trans. Fundamental