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.