The performance of optimal and some suboptimal lossless prefix encoding schemes for memoryless sources with a large alphabet size are studied. It is proved that the redundancy of the Huffman code for almost all sources with symbols is very close to that of the average distribution of the monotone sources with ymbols. This value lies between 0.02873 and 0.02877 bit for large .Our results show that this is also the case with the M coding scheme in which all -tuple sources with sorted-probabilities are encoded by the optimal code for the average distribution of monotone sources with ymbols. Thus, M coding is a near-optimal code for most sources witha large alphabet. Also, it is shown that the redundancy of the Shannon codeis very close to 0.5 bit for most sources with ymbols. The redundancy of the Fixed-length code, Uniform code and SU coding scheme are also studied.Itis proved that, for the aforementioned encoding scheme, the redundancy of most sources with symbols is very close to the average redundancy over the set of sources with ymbols.For a large alphabet size ,these values can be approximated by some functions of the fraction part of .
