The greatest difficulty of compressing data is the assurance of the security, integrity, and accuracy of the data in storage in volatile media or transmission in network communication channels. Various methods have been proposed for dealing with the accuracy and consistency of compressed and encrypted data using error detection and correction mechanisms. The Redundant Residue Number System (RRNS) which is a trait of Residue Number System (RNS) is one of the available methods for detecting and correcting errors which involves the addition of extra moduli called redundant moduli. In this paper, Residue Number System (RNS) is efficiently applied to the Lempel-Ziv-Welch (LZW) compression algorithm resulting in new LZW-RNS compression scheme using the traditional moduli set, and two redundant moduli added resulting in the moduli set {2^n-1,〖 2〗^n,〖 2〗^n+1,〖 2〗^2n-3,〖 2〗^2n+1} for the purposes of error detection and correction. This is done by constraining the data or information within the legitimate range of the dynamic range provided by the non-redundant moduli. Simulation with MatLab shows the efficiency and fault tolerance of the proposed scheme than the traditional LZW compression method and other related known state of the art schemes.
This paper proposes an efficient residue to binary converter on a new three-moduli set (2 2 +1 , 2 2 +1 − 1, 2 − 1) using the Mixed Radix Conversion. The proposed reverse converters are adder based and memoryless. In comparison with other moduli sets with similar dynamic range, the new schemes out-perform the existing schemes in terms of both hardware cost and propagation delay.
Number Systems are media for representing numbers; the popular ones being the Weighted Number Systems (WNS), which sometimes propagate carries during arithmetic computations. The other category, Un-Weighted Number Systems, of which the Residue Number System (RNS) belongs, do not carry weights but have not yet found widespread usage in general purpose computing as a result of some challenges; one of the main challenges of RNS is overflow detection and correction. The presence of errors in calculated values due to such factors as overflow means that systems built on this number system will continue to fail until serious steps are taken to resolve the issue. In this paper, a scheme for detecting and correcting overflow during RNS addition is presented. The proposed scheme used mixed radix digits to evaluate the magnitude of the addends in order to detect the occurrence of overflow in their sum. The scheme also demonstrated a simplified technique of correcting the overflow in the event that it occurs. An analysis of the hardware requirements and speed limitations of the scheme showed that it performs considerably better in relation to similar state of art schemes.
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