As newly invented packet erasure codes, digital fountain codes (LT codes and Raptor codes) under iterative message passing decoding can work very efficiently in computer networks for large scale data distribution (e.g., greater than 64000 bits) without knowledge of the states of individual lossy channels, regardless of the propagation modes. Some researchers have moved further and found that fountain codes can achieve near capacity performance over AWGN channels. However, little literature on the research of a fountain code’s decoding overhead had been obtained, especially for short and moderate-length data (e.g., smaller than 10000 bits). We are interested in the overheads of fountain codes of different kinds or designs because a harsh communication condition can hurt some decoding schemes by limiting the number of received encoded symbols. Moreover, we have only found in literature studies of Raptor codes whose precodes are rate 0.98 left-regular, right-Poisson LDPC codes, but performance with other types of pre-codes is unknown. In this dissertation, we review conventional fountain codes and describe two system models for packet erasure fountain codes and bit error correcting fountain codes under message passing decoding over binary erasure channels or AWGN channels. We assess Raptor codes with different kinds of pre-codes, introduce maximum likelihood decoding to both LT codes and Raptor codes, and propose a hybrid message passing and fast maximum likelihood decoding algorithm for LT codes. Our simulation results show that error rate and overhead depends on both decoding algorithm and pre-code characteristics. In general, maximum likelihood decoding consumes much less overhead than message passing decoding. Our hybrid algorithm can realize very low overhead with short-length LT codes but still enable fast decoding. LT codes can decrease the fraction of overhead as data length grows but Raptor codes may not. A higher rate pre-code can accomplish better performance of Raptor codes than a lower rate pre-code, and the structure of the pre-code may not matter.
|Commitee:||Dill, Jeffrey, Irwin, Dennis|
|Department:||Electrical Engineering (Engineering and Technology)|
|School Location:||United States -- Ohio|
|Source:||DAI-B 78/11(E), Dissertation Abstracts International|
|Subjects:||Computer Engineering, Engineering, Electrical engineering|
|Keywords:||Fountain code, LDPC codes, LT codes, Maximum likelihood, Message passing, Raptor code|
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