Arithmetic coding, in conjunction with a suitable probabilistic model, can provide nearly optimal data compression. In this article we analyze the effect that the model and the particular implementation of arithmetic coding have on the code length obtained. Periodic scaling is often used in arithmetic coding implementations to reduce time and storage requirements; it also introduces a recency e...

This paper clari es two variable-toxed length codes which achieve optimum large deviations performance of empirical compression ratio. One is Lempel-Ziv code with xed number of phrases, and the other is an arithmetic code with xed codeword length. It is shown that Lempel-Ziv code is asymptotically optimum in the above sense, for the class of nite-alphabet and nite-state sources, and that the ar...

It is well-known that for a given sequence, its optimal codeword length is fixed. Many coding schemes have been proposed to make the codeword length as close to the optimal value as possible. In this paper, a new block-based coding scheme operating on the subsequences of a source sequence is proposed. It is proved that the optimal codeword lengths of the subsequences are not larger than that of...

Redundancy is de ned as the excess of the code length over the optimal (ideal) code length. We study the average redundancy of an idealized arithmetic coding (for memoryless sources with unknown distributions) in which the Krichevsky and Tro mov estimator is followed by the Shannon{Fano code. We shall ignore here important practical implementation issues such as nite precisions and nite bu er s...

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

Most existing alias analysis techniques are formulated in terms of high-level language constructs and are unable to cope with pointer arithmetic. For machines that do not have ’base + offset’ addressing mode, pointer arithmetic is necessary to compute a pointer to the desired address. Most state of the art compilers such as GCC lack the mechanism to determine aliasing between such computed poin...

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid the excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding r...

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid the excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding r...