Abstract: Considering that the Code-Aided (CA) carrier recovery algorithms perform small synchronization range and big inaccuracy in extremely low Signal to Noise Ratio (SNR) deep space communication systems, two joint assisted carrier synchronization algorithms by code and pilot are proposed. First the Log-Likelihood-Function (LLF) of CA carrier estimation is derived by Maximum-Likelihood (ML) criterion and two new CA fine synchronization algorithms which have closed-form expression are got by simplify the Maclaurin series of LLF and its derivative. And then, a coarse synchronization algorithm is proposed based on pilot symbols in order to handle larger parameter offsets and its Mean Squared Error (MSE) is also derived. Finally, two joint assisted carrier synchronization algorithms by code and pilot are got by orderly combining the coarse estimation algorithm and fine estimation algorithm. And the simulations by the LDPC-Hadamard code with rate 1/12 verify that the new algorithm can increase synchronization range and improve accuracy, achieving perfect synchronization with a certain amount of pilot symbols at extremely low SNR.