One of the most important features of an appropriate code for a lot of standards is the ability of being decoded instantaneously. That’s why prefix-free codes have been introduced. But these codes, which could be decoded only in one direction (forward), are vulnerable to bit errors. Fix-free codes, which could be decoded in both forward and backward directions, were introduced to significantly mitigate this problem. Therefore their decoding speed will get doubled and their error-resilient capabilities will be enhanced. But it is not easy to find a fix-free code with the minimum redundancy (optimum), in the other words, the most compressed one. The algorithm of finding the optimal fix-free code, studied in this thesis, has been proposed about two years ago. But a new sub-optimal algorithm has been proposed in this thesis to find an appropriate symmetric fix-free code because the optimal one needs a lot of memory and time. ( In this thesissymmetric fix-free codes have been focused). Th e proposed algorithm is faster and easier to implement than optimal algorithm because its search space is smaller. Its output codes for the English alphabet (with 26 symbols) and average distribution (with 1-100 symbols) have been analyzed and they are same as optimums. Then it has been proven that in the case of unknown probability vector selected from monotone sources set by the uniform probability function, the best fixed-length vector independent of probability vector for any source with N symbols is the optimal code of average distribution by the Minave criterion. But, because of difficulties in finding the optimal code, sub-optimal algorithm could be used. Hence, the structure of sub-optimal code for average distribution has been analyzed and some closed-form formulas have been found for its multiplicity vector. Eventually, lower and upper bounds on average redundancy of optimal symmetric codes have been proposed. Using this lower bound, it has been demonstrated that proposed algorithm will construct an appropriate code close to optimal one, for average distribution with more than 100 symbols too. In addition, lower bound showed the redundancy of symmetric fix-free code is more than Huffman code and goes to infinity as it had been proven formerly. Key Words: Source Coding, Redundancy, Symmetric Fix-free Code, Average Distribution.