LT codes decoding: Design and analysis

LT codes provide an efficient way to transfer information over erasure channels. Past research has illustrated that LT codes can perform well for a large number of input symbols. However, it is shown that LT codes have poor performance when the number of input symbols is small. We notice that the poor performance is due to the design of the LT decoding process. In this respect, we present a decoding algorithm called full rank decoding that extends the decodability of LT codes by using Wiedemann algorithm.We provide a detailed mathematical analysis on the rank of the random coefficient matrix to evaluate the probability of successful decoding for our proposed algorithm. Our studies show that our proposed method reduces the overhead significantly in the cases of small number of input symbols yet preserves the simplicity of the original LT decoding process.