Single Feedback Shifted LT Codes With Joint Channel Coding

In wireless communication, inevitable noise interference in the channels causes packet loss frequently. Digital fountain codes, which are a class of error correcting codes for the erasure channel, become a hotspot since their properties of strong error correction capability and high coding efficiency. However, with original degree distribution, the decoding overhead of fountain codes can still be reduced, and it should be further studied to improve the efficiency of communication. Some studies have shown that multiple feedbacks fountain codes can reduce the decoding overhead. However, excessive feedbacks will cost a lot of channel resources. For the tradeoff between decoding overhead and channel resources, a study on feedback fountain codes is proposed in this dissertation. This work focuses on three aspects:the number of feedback reduction, the degree distribution design and the message propagation (MP) decoding method. The main contributions are outlined as follows.First, an adaptive single feedback shifted Luby transform (SLT) codes with channel coding is proposed to save channel resources for multiple feedbacks problem. Luby transform (LT) codes are used to correct error packets at the receiver, and feedback information from receiver is adopted to adjust the degree distribution in order to reduce the uncertainty of source information. Then we can get the single feedback SLT codes. Correct symbols in error packets can be used for correction, so as to restore more information. Therefore, when there are enough redundancy coding symbols in the channel, using correct symbols of the error packets and correlation between packets to correct error in MP decoding, more than one adjacent error packets can be recovered simultaneously with one encoding packet. This coding method is called single feedback SLT codes with joint channel coding. The simulation results show that the number of packets sent from the source in this signal feedback coding method is much less than that in original LT codes.Second, in order to deal with the changes of coding structure in feedback fountain codes, an improved shifted robust soliton distribution (ISRSD) and an expand shifted robust soliton distribution (ESRSD) are designed for single feedback SLT codes and feedback SLT codes with joint channel coding. Since shifted robust soliton distribution (SRSD) still has large decoding overhead in single feedback SLT codes, ISRSD degree distribution is a modified SRSD using the optimum monomial degree distribution with less decoding overhead. Experiments show that ISRSD is superior to SRSD for the single feedback SLT codes and single feedback SLT codes with joint channel coding. Because single feedback SLT codes with joint channel coding has an ability of mutiple adjacent error packets recovery. Which is not considered in ISRSD, there should be a probability distribution for recovering multiple adjacent error packets in the degree distribution design. Considering the impact of this probability distribution on ideal soliton distribution, an ESRSD is proposed by shifting the degree distribution with the feedback information according to the SRSD degree distribution. Simulations show that ESRSD degree distribution is superior to I SRSD and SRSD in single feedback SLT codes with joint channel coding.Finally, this thesis proposes an MP decoding method based on linear block codes for decoding the single feedback SLT codes with joint channel coding. On the basis of MP decoding, a code matrix is constituted with coding packets and multiple adjacent error packages. This method uses LT coding address for column parit, and recovers error packets with delete method and substitution method in error location.And it guarantees the accuracy with verifying the checking matrix of a linear block code. This decoding method ensures that one encoding packet can recover more than one error packets after the iteration, and it improve the decoding performance of fountain codes.The proposed feedback fountain codes develop the degree distribution with only one feedback. It does not only reduce the resources occupation of feedback channel, but also takes full advantage of redundant information of coding channel to decode, and to improve coding efficiency.