New Error Control Algorithms for Residue Number System Codes

Xiao, Hanguang; Garg, H.K.; Hu, Jianhao; Xiao, Guoqiang

doi:10.4218/etrij.16.0115.0575

Cited by 18 publications

(15 citation statements)

References 17 publications

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“…Here q i is the same notation as Algorithm 1 and satisfies q il = q i M l for l ∈ G . However, in the worst case that all labels of γ j in I t are from G and |B| = |R t | = L−K 2 , after residue sets removed, it is reduced to a system with L− L−K When we apply list decoding [7], [2] to correct up to L−K 2 errors in each step of GCRTMN [8] on q il , it is not guaranteed that q i can be uniquely recovered from q il . Nevertheless, q i should be in the decoding list since…”

Section: A Folding Number Estimationmentioning

confidence: 99%

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On Solving Ambiguity Resolution With Robust Chinese Remainder Theorem for Multiple Numbers

Xiao

2019

IEEE Trans. Veh. Technol.

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Chinese Remainder Theorem (CRT) is a powerful approach to solve ambiguity resolution related problems such as undersampling frequency estimation and phase unwrapping which are widely applied in localization. Recently, the deterministic robust CRT for multiple numbers (RCRTMN) was proposed, which can reconstruct multiple integers with unknown relationship of residue correspondence via generalized CRT and achieves robustness to bounded errors simultaneously. Naturally, RCRTMN sheds light on CRT-based estimation for multiple objectives. In this paper, two open problems arising that how to introduce statistical methods into RCRTMN and deal with arbitrary errors introduced in residues are solved. We propose the extended version of RCRTMN assisted with Maximum Likelihood Estimation (MLE), which can tolerate unrestricted errors and bring considerable improvement in robustness.

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Section: A Folding Number Estimationmentioning

confidence: 99%

“…In [2], Guruswam et al proved that there still exists polynomial time list decoding scheme of remainder code when λ < L − √ KL. For general λ, the corresponding results can be refereed in [7]. We will use the above results in the following proof.…”

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confidence: 97%

On Solving Ambiguity Resolution With Robust Chinese Remainder Theorem for Multiple Numbers

Xiao

2019

IEEE Trans. Veh. Technol.

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“…The Lagrange form of remainder makes analysis of truncation errors easier and we can approximate the major conceivable truncation error through analyzing Rm n . Taylor series of a function f at 0 is also called as the Maclaurin series of f fðxÞ ¼ e x (12) Truncation part (TP) errors are named as quantization error or truncation error that results by means of an estimate in an exact mathematical process of Taylor series (Maclaurin series) which is given by…”

Section: Taylor-series Expansion Algorithmmentioning

confidence: 99%

“…10,11 Error control algorithms for redundant residue number systems and residue number system (RNS) product codes have a computational complexity of obtaining error values inside an arrangement of qualities. 12 The proposed design involves residue logarithmic number system (RLNS) to design FP multiplier. RLNS is the combination of both RNS and LNS.…”

Section: Introductionmentioning

confidence: 99%

A high-speed fixed width floating-point multiplier using residue logarithmic number system algorithm

Rubia¹,

Sathishkumar²

2018

The International Journal of Electrical Engineering & Educa

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The Residue Logarithmic Number System (RLNS) in digital mathematics allows multiplication and division to be performed considerably quickly and more precisely than the extensively used Floating-Point number setups. RLNS in the pitch of large scale integrated circuits, digital signal processing, multimedia, scientific computing and artificial neural network applications have Fixed Width property which has equal number of in and out bit width; hence, these applications need a Fixed Width multiplier. In this paper, a Fixed Width-Floating-Point multiplier based on RLNS was proposed to increase the processing speed. The truncation errors were reduced by using Taylor series. RLNS is the combination of both the residue number system and the logarithmic number system, and uses a table lookup including all bits for expansion. The proposed scheme is effective with regard to speed, area and power utilization in contrast to the design of conservative Floating-Point mathematics designs. Synthesis results were obtained using a Xilinx 14.7 ISE simulator. The area is 16,668 µm2, power is 37 mW, delay is 6.160 ns and truncation error can be lessened by 89% as compared with the direct-truncated multiplier. The proposed Fixed Width RLNS multiplier performs with lesser compensation error and with minimal hardware complexity, particularly as multiplier input bits increment.

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“…The residue number system (RNS), initially proposed in 1959, was derived from the third century Chinese remainder theorem [1]. RNS architectures are now applied in many growing fields such as cryptography [2], image-processing systems [3], and error-correction codes [4] due to its convenience in parallel computing. Parallel processing with RNS often involves replacing a typical base-2 system with a different number representation system built upon two or more coprime number bases, which we refer to as mixed-radix (MR) [5].…”

Section: Introductionmentioning

confidence: 99%

Shannon Entropy Loss in Mixed-Radix Conversions

Vennos

Michaels

2021

Entropy

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This paper models a translation for base-2 pseudorandom number generators (PRNGs) to mixed-radix uses such as card shuffling. In particular, we explore a shuffler algorithm that relies on a sequence of uniformly distributed random inputs from a mixed-radix domain to implement a Fisher–Yates shuffle that calls for inputs from a base-2 PRNG. Entropy is lost through this mixed-radix conversion, which is assumed to be surjective mapping from a relatively large domain of size 2J to a set of arbitrary size n. Previous research evaluated the Shannon entropy loss of a similar mapping process, but this previous bound ignored the mixed-radix component of the original formulation, focusing only on a fixed n value. In this paper, we calculate a more precise formula that takes into account a variable target domain radix, n, and further derives a tighter bound on the Shannon entropy loss of the surjective map, while demonstrating monotonicity in a decrease in entropy loss based on increased size J of the source domain 2J. Lastly, this formulation is used to specify the optimal parameters to simulate a card-shuffling algorithm with different test PRNGs, validating a concrete use case with quantifiable deviations from maximal entropy, making it suitable to low-power implementation in a casino.

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New Error Control Algorithms for Residue Number System Codes

Cited by 18 publications

References 17 publications

On Solving Ambiguity Resolution With Robust Chinese Remainder Theorem for Multiple Numbers

On Solving Ambiguity Resolution With Robust Chinese Remainder Theorem for Multiple Numbers

A high-speed fixed width floating-point multiplier using residue logarithmic number system algorithm

Shannon Entropy Loss in Mixed-Radix Conversions

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