一种基于模运算和扩展欧几里得定理的喷泉码

针对中国剩余定理在模运算喷泉码译码过程中的固有不足，本文提出一种全新的基于扩展欧几里德定理的译码算法.该算法采用合并线性同余方程组，避免分解因子非互质情况下求解乘率因子失败的问题.模运算喷泉码将信息数据编码为自然数分解因子和相对应的模余数的数据包，接收方只要获取一定数目的编码数据包就能成功解码.基于扩展欧几里得定理的译码算法扩展了模运算喷泉码的分解因子范围，提高了编译码效率.本文通过理论分析和数值仿真证实了这种编译码算法的可行性.

Novel Fountain Codes Based on Modulo and Extended Euclidean

Aiming at the intrinsic problems of Chinese Remainder Theorem in fountain decoding process with modular arithmetic,this paper proposes a decoding algorithm based on extended Euclidean theorem.The linear congruence equations are merged in the extended Euclidean decoding algorithm,which avoids the failure of solving the rate factor when the decomposition factors are non-coprime.In the modular arithmetic fountain encoding process,the original packet is continuously decomposed by the factor,which is randomly selected from the natural number,into the encoded packets consisting of the residues and the factors.When a certain amount of packets are received,it can be achieved to decode successfully.The codec efficiency has been improved as the algorithm has extended the range of the modular arithmetic factor.Through theoretical analysis and numerical simulation,the effectiveness of this decoding algorithm of modular arithmetic fountain code has been proved.