LT code : decoding algorithm and its applications
Haifeng Lu · 2015
Reliable transmission over error-prone channels is always a problem for network researchers.To control errors in transmissions, the technique Forward Error Correction (FEC) was proposed in 1940s.Among different coding schemes, Reed-Solomon and Low Density Parity Check codes are the most successful ones.Although these codes can achieve channel capacity, the performance relies on knowledge of channel condition since the coding rate is determined beforehand.To overcome this, fountain codes were proposed.For a given number of source symbols, fountain codes can generate potentially limitless encoded symbols.Luby Transform (LT) codes are the first realizations of fountain codes.The low complexity of both encoding and decoding makes LT codes applicable in many different applications from data transmission to storage system.This thesis is dedicated to improve LT decoding algorithm under certain circumstance and apply LT codes in multimedia transmission and in cloud storage system.Past research has shown that LT codes can perform well for a large number of source symbols.However, mathematical analysis and simulation results have revealed that the packet overhead for LT decoders can be as large as 100% when the number of source symbols is small.LT-W decoding was proposed to tackle this problem.In the first part of this thesis, we make an observation that LT decoders often fail to recover all the source symbols, while LT encoders have a high probability of producing a full-rank coefficient matrix.Through rigorous analysis and extensive experiments, we show that LT-W decoding can dramatically reduce the overhead for LT codes with small input symbol.LT codes have been proven successful in content delivery due to their abilities to handle varying channel conditions without much feedback.However, original LT codes are RS codes Reed-Solomon codes LDPC codes Low-Density-Parity-Check codes