An improved LT encoding scheme with extended chain lengths

The BP decoding terminates frequently during the early stage for LT codes with the robust Soliton distribution. Generally, more than 90% of undecoded input symbols result from decoding termination within the range 0 ≤ n ≤ k/2, where n and k are the decoded and total number of input symbols, respectively. This study focuses on reducing the symbol loss probability by preventing early decoding termination. Input symbols can be divided into decoding chains with respect to the connectivity of degree-2 encoding symbols such that neighbors of a degree-2 encoding symbol belong to the same decoding chain. The number of input symbols in a decoding chain is called the chain length. It is found that the average chain length is shorter if the decoding termination occurs within 0 ≤ n ≤ k/2. We propose an encoding scheme which increases the chain length to avoid early decoding termination. Each code block is divided into two groups - the first one contains τ randomly selected input symbols, while the rest k - τ symbols form the second group. Neighbors of any degree-2 encoding symbol are restricted from different groups of input symbols. The probability that two degree-2 encoding symbols have a neighbor in common is increased, leading to longer decoding chain on average. Simulation results show that the symbol loss probability of the proposed encoding scheme is always lower than that of the LT encoding. The improvement by our scheme in the symbol loss probability increases with k. In comparison with the LT encoding, when the overhead is sufficiently large, the proposed scheme also achieve higher probability of successful decoding.