We address the problem of construct- ing an adaptive a rithmetic code in the case where the source alphabet is large and there are lots of different symbols with equal counts of occurrence. For an al- phabet of N symbols and T distinct symbol weights we describe a code for which the number of operations of encoding and decoding is equal to clog r + c1 instead of clog N + c2 as in previous arithmetic codes, c, c1, c2 are constants. When T is small relative to N - which is the case for most practical coding problems on large alphabets - the encoding and decoding speed of the suggested code will be substantially greater than with known methods. Arithmetic coding was introduced by Rissanen (GI and now it is one of the most popular methods of source coding. The
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