Error correction based on redundant Residue Number System

Turbo decoded redundant residue number system (RRNS) codes are proposed and their performance is evaluated. An RRNS (n,k) code is a maximum-minimum distance block code, exhibiting identical distance properties to Reed-Solomon (RS) codes. Hence their error correction capability is given by t=(n-k)/2. We adapt the classic Chase algorithm in order to accept soft inputs and to provide soft outputs. Using the proposed soft input soft output (SISO) Chase algorithm, the turbo decoding of RRNS codes is contrived.

The so called Residue Number System (RNS) and redundant residue number system (RRNS) has improved systems in high speed parallel signal processing structures and the RRNS has also been widely employed for self-cheking, error-detection and error- correction in digital processors, arithmetic units and data transmission [1–5].

The architecture of a fault-tolerant modular neurocomputer based on modular number projections

In this paper, two error-correcting algorithms for redundant residue number systems are presented, one for single residue-error correction and the other for burst residue-error correction. Neither algorithm requires table look-up and hence their implementations need a memory space which is much smaller than that required by existing methods. Furthermore, the conditions which the moduli of the redundant residue number systems must satisfy in these two algorithms are less restrictive than that of existing methods. Comparison of the approach on which these two algorithms are based and that of existing methods is given.

Fault-tolerant data transmission models based on the redundant residue number system are proposed in this paper; they can transmit data correctly between two ends unless the residue errors exceed the error-correction capability. The expressions for the probability of error are presented when the channel noise is additive Gaussian noise and each branch is M-ary orthogonal signaling modulation. The expressions of the probabilities of undetected and uncorrected error are also obtained when the redundant residue number system are single error-checking and single error-correcting model, respectively.

Residue arithmetic offers a new approach to the development of general-purpose digital computers which detect and correct their own arithmetic and data-transmission errors. This approach is based on special properties inherent in a suitably chosen redundant residue number system (RRNS). In this paper, RRNS algorithms are described which can detect any number of residues in error, and can detect and correct one residue in error, in a data word suitable for scientific or control computation. Moreover, it is shown that there are RRNS algorithms available to perform all arithmetic operations needed in ordinary general-purpose computation. To this end, a new class of residue arithmetic techniques based on the properties of "macro-coefficients" is introduced, which permits all required fractional operations to be carried out and leads to a convenient form of the error-detection-and-correction procedures. The implications of these developments for ultra-reliable computer design are discussed, and the RRNS approach to computer ultrareliability is compared with several others which have been suggested; binary information with a residue check digit (BRCD), linear codes, and logic-circuit-level redundancy techniques such as majority voting.

In spite of rapid advances during the last few years in the design and realization of digital filters, very little attention has been given to the problems of error detection and correction in digital filters. This paper describes how redundant residue number system properties can be used for this purpose. The theory is presented with special emphasis on overflow detection, error correction, and gradual system degradation in the presence of recurring errors. A filter simulation program is described and simulation results are presented to illustrate the principles in recursive digital filters.

Mixed Radix Conversion is an essential feature of error detection and correction in Redundant Residue Number Systems. Fermat numbers are a popular choice as moduli in these systems. However, Fermat numbers are typically implemented using Diminished-1 arithmetic which necessitates special consideration of zero in arithmetic operations. Furthermore, the sequential nature of Mixed Radix Conversion leaves it prone to considerable delay due to carry propagation in adders at each stage. In this paper, Diminished-1 arithmetic in carry save form is used to give significant reductions in area and delay compared to previously proposed hardware architectures. The percentage area reduction was found to range from 13% to 41% and that of delay from 19% to 49% for bit widths from 8 to 28bits.

Big data becomes the key for ubiquitous computing and intelligence, and Distributed Storage Systems (DSS) are widely used in large-scale data centers or in the cloud for efficient data management. However, the data on stored are likely to be unavailable due to hardware failures and cyberattacks, e.g. DDoS. Maximum Distance Separable (MDS) codes are commonly used for the recovery of faulty storage nodes or unavailable data. However, the recovery of data nodes usually involves access to multiple nodes, which introduces significant communication overheads to the DSS. In this paper, a new DSS based on the Redundant Residue Number System (RRNS) is proposed, where efficient recovery is enabled by applying the second version of Chinese Remainder Theorem (CRT-II). The complexity and network traffic of the proposed data protection scheme is analyzed theoretically and compared with that of traditional MDS based DSSs. Experimental results show that the proposed DSS achieves lower encoding complexity, lower recovery complexity and lower network traffic than the MDS based schemes. Although the proposed data protection scheme introduces computation overheads for the case on which there are no failing nodes, its complexity is still lower for scenarios with frequent data updates. In addition, the proposed scheme introduces additional advantages in terms of security and storage flexibility.

In WSI, a single noise could disrupt the system. However, neither dual system nor triple system can be used as a countermeasure because WSI benefits from the use of a single wafer system. This paper presents a design procedure for noise‐tolerant systems in which multiple clock pulses and the features of the residue number system are effectively combined. The design sequence is as follows: (1) The system is designed based on the redundant residue number system. (2) The circuits corresponding to the digits of the residue number system are driven by the clock pulses, each of which has a different phase. (3) A circuit is applied which corrects the noise‐induced error through calculation of the remaining correct digits. The reliability of a nonrecursive digital filter is clearly improved by applying the given method. The reliability is, however, reduced by pipelining and the hardware upgrade needed for redundancy is limited to 31%. By applying the given method, coincident noise‐induced faults throughout the system are avoided and the redundant hardware is reduced. We have found the method suitable for noise‐tolerant systems design of WSI.

A novel multi-code direct-sequence code division multiple-access (DS-CDMA) system based on the so-called residue number system (RNS) or the redundant residue number system (RRNS) is proposed. Concatenated codes employing RNS product codes (RNS-PC) as the inner codes and non-binary Reed-Solomon (RS) codes as the outer codes are adopted to improve the system performance. The results show that, for a given outer RS code and a given number of moduli of the inner RNS-PC, the performance of the system can be optimized by varying the relative number of information moduli and redundant moduli of the inner RNS-PC, as well as by appropriately choosing the moduli's values.

In this paper we introduce the idea of using Redundant Residue Number System (RRNS) codes in steganography, and we determine their embedding capacities. We take advantage of the redundancy parameter and the correction capacity of RRNS codes, i.e., we hide secret data in some residues in such way that the altered number of residues does not exceed half the redundancy of the code.

A new approach, based on redundancy techniques to detect residue arithmetic overflow, is presented. The detection, when applied to residue systems having residue-to-binary decoders, only requires an additional residue encoder to function.

In order to get an efficient comprehensive analysis on Doppler estimation in RADAR; need an enhanced arithmetic formulation procedure for density, power and latency optimisations. Modular adders and multipliers are very crucial components in the performance of residue number system-based applications. The Residue Number System (RNS) is a non-positional number system that allows parallel computations without transfers between digits. However, some operations in RNS require knowledge of the positional characteristic of a number. Among these operations is the conversion from RNS to the positional number system. The methods of reverse conversion for general form moduli based on the Chinese remainder theorem and the mixed-radix conversion are considered, as well as the optimized methods for special form moduli. A modified New CRT-I & New CRT-II with conjugate moduli set is considered to implement adder, multipliers and subtractions with optimised algorithms. This paper mainly deals with the conversion of numbers from binary to RNS as well RNS to binary with the specific modulo {2^n±k} which proves this new method. Modified Radix16 booth encoding algorithm and square carry bypass adder are used in implementation of RNS system to reduce parameter constraints.

Creation of reliable and secure cloud storage is a complicated task, since this type of data storage and processing is efficient and cost effective. The Residue Number System (RNS) can be used to achieve the required level of data security and reliability. RNS is a non-positional number system, the use of which for data protection is promising. Redundant RNS allows the creation of correction codes. Such properties of error-correction codes as effectiveness, safety and reliability depend on the redundancy of the RNS. This paper evaluates the effectiveness of the RNS correction codes usage in multi-cloud data storage and processing systems by examining various sets of RNS moduli.