A Study Of Combination Algorithm On Combined Error Correcting Codes

With the development of digital media delivery technology and the popularization of the mobile intelligent terminal, the requirement of mobile video service especially the mobile video service carried by smartphone is growing exponentially. The rapidly increasing mobile video traffic causes great challenge to the communication system. In order to meet the user experience, it is needed to enhance the rate of data recovery with the premise of reliable and efficient as much as possible. So Evolved Multimedia Broadcast Multicast Service(e MBMS) based on mobile telecommunication networks has become a research hotspot.Application Layer FEC(AL-FEC) is brought into the e MBMS to protect the system from erasures. The packet with checksum error will be discarded in the data recovery. However these data packets still contain a mass of available information. In the paper, we investigate the comprehensive utilization of these erasure errors. In order to improve the recovery rate of the video streaming, AL-FEC codes in conjunction with Physical Layer FEC(PHY-FEC) codes is investigated.In the paper, a joint error correction model is established by means of the analysis of the AL-FEC and PHY-FEC. The model discards the error detection mechanisms in the AL-FEC package and makes use of all the received packages to resume the original message. According to the packet header, this paper proposes two directions of the joint error correction. One is based on a random generator matrix and the other is based on a certain generator matrix.For the random aspect, we find two theoretical bounds of the code length and put forward a merging algorithm. Firstly, by discussing the decoding probability under random linear fountain codes, a bound of code length is given, which provide a proper opportunity of decoding. Secondly, the Compound Channel model is introduced to describe the characteristic of the joint error correction channel. Combined with Shannon information theory, an upper bound of the code rate is given. Thirdly, learning with errors(LWE) is analyzed in this paper and the joint error correction under the random generator matrix is formulated as a difficult problem in cryptography. So there is no low-complexity algorithm in the finite field. Finally, having studied the degraded LWE problem, this paper puts forward a merging algorithm based on least square method. Comprehensive utilization of numerical mapping, least square method and constellation mapping has been made to complete the joint error correction.For the certain aspect, a framework of the joint error correction is proposed. Whereas the difficulties of the LWE problem, the generator matrix of the joint error correction code is derived from the traditional error-correcting codes—BCH codes or LDPC codes, providing a new direction of the code construction.At last, a simulation is made for the theoretical bounds and the merging algorithm. The performance of simulation shows that the combined error correcting scheme in the paper could make full use of the error packets and have considerable practical value.