A coding theory approach to error control in redundant residue number systems. II. Multiple error detection and correction

Sun, Jenn-Dong; Krishna, Hari

doi:10.1109/82.204107

Cited by 70 publications

(55 citation statements)

References 15 publications

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“…The RNS employs carryfree arithmetic which ensures that operations related to the different residue digits are independent. The errors during multiplication, addition and subtraction operations, or due to transmission or processing noise do not propagate and remain confined to their original residue digits and do not contaminate other residue digits [27]- [31]. Thus RNS arithmetic simplifies computations by decomposing a problem into a set of parallel residue computations.…”

Section: Rns and Rrns Based Channel Codingmentioning

confidence: 99%

“…In [54], an implementation of CRT using systolic array has been proposed which has a complexity of θ(logN P ), where N is the number of moduli and P is the number of bits. The Base Extension algorithm is used in [30], [31] with a complexity of O(N 2 ), where N is number of non-redundant moduli used in RRNS.…”

Section: Complexity Of Rrns-stbcmentioning

confidence: 99%

“…According to the CRT, any u-tuple residue representation (r 1 , r 2 , ..., r u ), where 0 ≤ r i ≤ m i for i = 1, 2, ..., u, there exists one and only one integer N such that 0 ≤ N ≤ M r and r i = N (modm i ). The numerical value of N can be computed according to the equation [23], [31]:…”

Section: Chinese Remainder Theoremmentioning

confidence: 99%

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Redundant residue number system based space-time block codes

Sengupta

Natarajan

2014

Physical Communication

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Space-time coding (STC) schemes for Multiple Input Multiple Output (MIMO) systems have been an area of active research in the past decade. In this thesis, we propose a novel design of Space-Time Block Codes (STBCs) using Redundant Residue Number System (RRNS) codes, which are ideal for high data rate communication systems. Application of RRNS as a concatenated STC scheme to a MIMO wireless communication system is the main motivation for this work. We have optimized the link between residues and complex constellations by incorporating the "Direct Mapping" scheme, where residues are mapped directly to Gray coded constellations. Knowledge of apriori probabilities of residues is utilized to implement a probability based "Distance-Aware Direct Mapping" (DA) scheme, which uses a set-partitioning approach to map the most probable residues such that they are separated by the maximum possible distance. We have proposed an "Indirect Mapping" scheme, where we convert the residues back to bits before mapping them. We have also proposed an adaptive demapping scheme which utilizes the RRNS code structure to reduce the ML decoding complexity and improve the error performance. We quantify the upper bounds on codeword and bit error probabilities of both Systematic and Non-systematic RRNS-STBC and characterize the achievable coding and diversity gains assuming maximum likelihood decoding (MLD). Simulation results demonstrate that the DA Mapping scheme provides performance gain relative to a Gray coded direct mapping scheme. We show that Systematic RRNS-STBC codes provide superior performance compared to Nonsystematic RRNS-STBC, for the same code parameters, owing to more efficient binary to residue mapping. When compared to other concatenated STBC and Orthogonal STBC (OSTBC) schemes, the proposed system gives better performance at low SNRs.

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Section: Rns and Rrns Based Channel Codingmentioning

confidence: 99%

Section: Complexity Of Rrns-stbcmentioning

confidence: 99%

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Redundant residue number system based space-time block codes

Sengupta

Natarajan

2014

Physical Communication

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“…Efficient error correcting algorithms are reported in [16][17][18], while an overview on RRNS is available in [19]. In the Dependable and Secure Data storage for mobile ad hoc networks (DS 2 ) [12] the mobiles cooperate by creating and sharing files.…”

Section: Redundant Residue Number Systemsmentioning

confidence: 99%

Dependable and Secure Data Storage in Wireless Ad Hoc Networks: An Assessment of DS2

Chessa

Pietro

Maestrini

2004

Wireless on-Demand Network Systems

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Abstract. DS2 is a dependable and secure data storage for mobile, wireless networks based on a peer-to-peer paradigm. DS 2 provides support to create and share files under a write-once model, and ensures data confidentiality and dependability by encoding files in a Redundant Residue Number System. The paper analyzes the code efficiency of DS 2 using a set of moduli allowing for efficient encoding and decoding procedures based on single precision arithmetic, and discusses the security issues. The comparison of DS 2 with the Information Dispersal Algorithm approach (IDA) shows that DS 2 features security features which are not provided by IDA, while the two approaches are comparable from the viewpoint of code efficiency and encoding/decoding complexity.

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“…The Residue Number System (RNS) that supports carry free, parallel, high speed, low power and secure computing is applied to enhance the Huffman coding technique with the moduli set (2 n-1 , 2 n ─1, 2 n +1, 2 n+1 ─1) is proposed in this research. RNS has the advantage of fast computation over other number systems due to its inherent features of parallelism, fault tolerance, carry free operations, and modularity [8], [9], [10], [16]. The inherent error correction ability and fast intensive-arithmetic capability is of essence in this paper.…”

Section: Introductionmentioning

confidence: 99%

The Huffman’s Method of Secured Data Encoding and Error Correction using Residue Number System (RNS)

Alhassan¹,

Saeed²,

Agbedemnab³

2015

CAE

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Over the centuries, information security has become a major issue. Encryption and decryption of data has recently been widely investigated and developed because there is a demand for a stronger encryption and decryption which is very hard for intrusion. Cryptography plays major roles in fulfilment of these demands. Many of researchers have proposed a lot of encryption and decryption algorithms. But most of the proposed algorithms encountered problems such as lack of reduced cost of data and error control mechanisms to maintain the security of data in the communication channel. In this paper, a highly secured data encryption and decryption scheme is proposed to enhance the Huffman"s method. The Residue Number System (RNS) is employed with four moduli set {2 n-1 , 2 n ─1, 2 n +1, 2 n+1 ─1} and two redundant moduli set {2 2n -3, 2 2n +1} for error handling using the concept of the traditional Huffman"s algorithm, where the frequency of occurrences of each character are used to generate binary codes. The proposed scheme allows for unreadable encrypted set of bits, except the intended recipient with the right moduli set can decrypt it, reduced cost of both data transmission and storage, and error detection and correction. General TermsInformation Security, Number System, and Compression Algorithm.

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A coding theory approach to error control in redundant residue number systems. II. Multiple error detection and correction

Cited by 70 publications

References 15 publications

Redundant residue number system based space-time block codes

Redundant residue number system based space-time block codes

Dependable and Secure Data Storage in Wireless Ad Hoc Networks: An Assessment of DS2

The Huffman’s Method of Secured Data Encoding and Error Correction using Residue Number System (RNS)

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