Distributed LT Codes

This thesis describes techniques to decompose LT codes (a class of rateless erasure correcting codes) into distributed LT (DLT) codes. DLT codes can be used to independently encode data from multiple sources in a network in a way such that, when the DLT symbols (binary strings) are combined at a common relay, the resulting sequence of symbols (called a modified LT (MLT) code) has erasure correcting properties similar to those of an LT code. In essence, DLT codes are designed so that the final stage of encoding for erasure correction can be carried out by a low-complexity relay that selectively XORs the symbols generated at each source and transmits the result to the sink.Specifically, code contructions are presented for two-source and four-source networks. It is shown that the DLT/MLT approach can yield substantial performance benefits compared with a competing strategy wherein each of the sources uses its own independent LT encoder and the resulting bit-strings are time-multiplexed through the relay. This enhanced performance is due primarily to the longer blocklengths that are made possible by the MLT approach; when the relay-to-sink link is the bottleneck, it is better to deliver one long MLT codeword to the sink than multiple shorter LT codewords.