Optimization and Delay Minimization of Channel Adaptive Scale Free LT Code for BEC with High Erasure Probability

Abstract

Luby transform (LT) code is the first rate-less fountain code to both mitigate the erasure problem. If the erasure probability is very high, the receiver will not get enough encoded symbols to decode and eventually the decoding may fail or take long time to decode. In this paper, a scale free LT codec is presented. If the channel status shows low probability of erasure, it will generate the minimum number of symbols to save network resources like bandwidth and power, but if the channel status shows high probability of erasure, more encoded symbols will be generated so that a receiver can collect sufficient number of symbols to decode the entire message. Again for higher probability of erasure of the BEC, the decoder will discard many packets and will take a long time to decode the encoded symbols correctly. This paper proposes a solution for the delay associated with high erasure probability on the binary erasure channel, and presents some distributions to optimize the number of overheads, average degree and decoding iterations for acceptable delay constraints arising from hardware implementation, and it is found that the delay can be minimized by approximately 61% applying the degree distributions and optimized iterations.