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Performance Analysis and Improvement of LT Codes over AWGN Channels

LT codes, the first universal erasure-correcting codes, have near-optimal performance over binary erasure channels for any erasure probability, but exhibit high bit error rate and error floor over the noisy channels. This paper investigated the performance of LT codes over the additive white Gaussian noise channels. We designed the systematic LT codes through reconstructing the bipartite graph and proposed a modification of the encoding scheme for the systematic LT codes to eliminate the cycles in generator matrix. With the proposed encoding scheme, the systematic LT codes are almost left-regular. Consequently, two types of the systematic LT codes, left-regular right-regular and left-regular right-irregular LT codes, were considered from the perspective of bit error rate. For the left-regular right-irregular LT code, we modified the degree distributions and proposed three kinds of check-node degree distributions. And then we analyzed the performance of the above-mentioned systematic LT codes with the proposed encoding scheme and different degree distributions. Simulations results show that the performance of the systematic LT codes with the proposed encoding scheme outperforms that of the conventional LT codes and the bit error rate of the systematic LT codes declines more than one order compared with that of the conventional LT codes. Finally, we proposed a class of the concatenated code, which serially concatenate the conventional LT codes with the systematic LT codes adopting the proposed encoding scheme. The performance of the proposed concatenated code was evaluated through simulations.