Research On Encoding And Decoding Algorithm And Application Of Fountain Codes

As wireless communication systems develop rapidly,users started to demand more reliable information transmission.And the answer to that is fountain codes,a channel coding technology that is based on erasure channels and has been widely used for reliable transmission.Underpinned by random coding.it's favored for its robustness,efficiency,relatively simple encoding and decoding.In addition,it has no constant code rate and doesn't relies on feedback channels to ensure reliable transmission and to respond to the ever-changing channels.That being said,it's degree distribution function and the algorithm for coding and decoding still need further improvement.Based on the fountain codes as the main body,for the low decoding efficiency,unfull rank coding matrix and application scenarios,we study it's degree distribution algorithm,encoding and decoding algorithm and reliable transmission scheme.The main research work is as follows:Firstly,for the low decoding efficiency of fountain codes,the MBRSD degree distribution algorithm optimizes the average size of the ripple by controlling the connection of degree one encoded packets so as to reduce the decoding time.However,due to the lackness of degree one encoded package,the IMBRSD degree distribution algorithm is proposed by combining the interpolation algorithm and the MBRSD degree distribution algorithm.The improved algorithm reduces the number of encoded packets required for successful decoding and reduces the bit error rate of the system.Secondly,because the unfull rank coding matrix can not be correctly decoded by the receiver,this paper process coding matrix before sending encoded packets.Augmented matrix is attached to coding matrix,then simplify this matrix and add some column vectors to the original matrix.The algorithm proposed by the paper reduces the failure probability of fountain code decoding.Thirdly,aiming at the problem that the fixed code rate can not match the real-time channel capacity,this paper applies the fountain code with full rank coding matrix to solve the problem of unreliable transmission in broadcast scheme.The sender calculates the deletion probability of the actual channel according to the number of correctly decoded packets that fed back by the receiver,and then adjusts the number of the encoded packet according to the actual channel condition.The transmission scheme can reduce the energy consumption caused by the feedback channel and realize the code rate matching the time-varying channel capacity,therefore it increasethe reliability of broadcasting.