General N-Tap Data Permutation Engine

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Magdi Mohamed

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Typical Use N=5 Tap Q-Filter Computations h 5 <h 2 < h 1 <h 3 < h 4 h 4 x 1 x 2 x 3 x 4 x 5 f 1 f 2 f 3 f 4 f 5 Window Slots Signal Value h 1 h 2 h 3 h 5 Density Generators i  h 5 h 2 h 1 h 3 h 4 Threshold Kernel Parameter  h(x i ) q(A  ) q({x 4 }) q({x 4 , x 3 }) q({x 4 , x 3 , x 1 }) q({x 4 , x 3 , x 1 , x 2 }) q({x 4 , x 3 , x 1 , x 2 , x 5 })=1.0 Case Adaptive Weight  A  q(  )=0.0 Total area is the Q-Filter output value

An Existing Technique Fast Q-Filter Sorting Execution for N=5 Tap Overlapping Windows Time Series Time Slot ,[object Object],[object Object],[object Object],9 8 7 6 5 4 3 2 1 8 1 6 4 2 7 5 3 9 1 4 3 2 5 1st-Index 3 2 5 1 4 2nd-Index 2 5 1 4 3 3rd-Index 1 4 3 2 5 4th-Index 5 3 2 1 4 5th-Index

Innovation An Indirect Sorting Hardware Architecture Using Threshold Decomposition Techniques 14 00 21 31 02 09 24 18 03 1 2 3 4 5 6 7 8 9 2 5 9 6 1 8 3 7 4 1 2 3 4 5 6 7 8 9

Simulation of Invention N=9 Tap Sorting of Random Real-Valued Digital Input Cases

Closest Prior Art Bitonic Sorting Network ,[object Object],[object Object],[object Object],(c) Sorting {4,8,1,3,2,7,5,6} by Bitonic Sort (a) +ve comparator (b) -ve comparator

Analyzing the Complexity Bitonic Sorting Network (BSN) Versus Data Permutation Engine (DPE) n 2 n 2 n 2 n log 4 n worst seq cost efficiency, e(n) = c(n) n 2 1 n 2 log 2 n worst seq time speedup, s(n) = t(n) n 2 n log 4 n overall cost, c(n) = t(n) p(n) n 2 n log 2 n number of processors, p(n) 1 log 2 n running time, t(n) DPE (Novel Art) BSN (Prior Art) Architecture Complexity

$Advantages of Invention Characteristics and Promises ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Sorting continues to consume sizeable fraction of the time on mainframe computers, accounting for roughly one quarter of the cycles. New interest in sorting has risen in the areas of digital filtering, network routing, and VLSI. Sorting has also additional importance to designers of parallel algorithms: it is frequently used to perform general data permutations, including random access read and random access write. These data movement operations can be used to solve problems in graph theory, computational geometry, signal and image processing in optimal or near optimal time.$

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General N-Tap Data Permutation Engine

1. General N-Tap Data Permutation Engine Magdi Mohamed Motorola Labs, PRR CoE 2006-08-29 An Indirect Sorting Hardware Architecture Using Threshold Decomposition Techniques

2. Typical Use N=5 Tap Q-Filter Computations h 5 <h 2 < h 1 <h 3 < h 4 h 4 x 1 x 2 x 3 x 4 x 5 f 1 f 2 f 3 f 4 f 5 Window Slots Signal Value h 1 h 2 h 3 h 5 Density Generators i  h 5 h 2 h 1 h 3 h 4 Threshold Kernel Parameter  h(x i ) q(A  ) q({x 4 }) q({x 4 , x 3 }) q({x 4 , x 3 , x 1 }) q({x 4 , x 3 , x 1 , x 2 }) q({x 4 , x 3 , x 1 , x 2 , x 5 })=1.0 Case Adaptive Weight  A  q(  )=0.0 Total area is the Q-Filter output value

4. Innovation An Indirect Sorting Hardware Architecture Using Threshold Decomposition Techniques 14 00 21 31 02 09 24 18 03 1 2 3 4 5 6 7 8 9 2 5 9 6 1 8 3 7 4 1 2 3 4 5 6 7 8 9

5. Simulation of Invention N=9 Tap Sorting of Random Real-Valued Digital Input Cases

7. Analyzing the Complexity Bitonic Sorting Network (BSN) Versus Data Permutation Engine (DPE) n 2 n 2 n 2 n log 4 n worst seq cost efficiency, e(n) = c(n) n 2 1 n 2 log 2 n worst seq time speedup, s(n) = t(n) n 2 n log 4 n overall cost, c(n) = t(n) p(n) n 2 n log 2 n number of processors, p(n) 1 log 2 n running time, t(n) DPE (Novel Art) BSN (Prior Art) Architecture Complexity

8. How Big is the Saving in Cost? BSN DPE

General N-Tap Data Permutation Engine

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