Development of two new mean codeword lengths

Two new mean codeword lengths L(α, β) and L(β) are defined and it is shown that these lengths satisfy desirable properties as a measure of typical codeword lengths. Consequently two new noiseless coding theorems subject to Kraft’s inequality have been proved. Further, we have shown that the mean codeword lengths L1:1(α, β) and L1:1(β) for the best one-to-one code (not necessarily uniquely decodable) are shorter than the mean codeword length LUD(α, β) and LUD(β) respectively for the best uniquely decodable code by no more than logDlogDn + 3 for D = 2. Moreover, we have studied tighter bounds of L(α, β).