Difference between revisions 108480323 and 108480330 on dewiki

In [[computational complexity theory|complexity theory]], the class '''NC''' (for "Nick's Class") is the set of [[decision problem]]s decidable in [[polylogarithmic time]] on a [[parallel computing|parallel computer]] with a polynomial number of processors.  In other words, a problem is in '''NC''' if there exist constants ''c'' and ''k'' such that it can be solved in time [[Big O notation|(contracted; show full)

# <math>\textbf{NC}^1 \subset \cdots \subset \textbf{NC}^i \subset \cdots \subset \textbf{NC}</math>
# <math>\textbf{NC}^1 \subset \cdots \subset \textbf{NC}^i = \cdots = \textbf{NC}</math>

It is widely believed that (1) is the case, although no proof as to the truth of either statement has yet been discovered.


==Algorithm Projects Proof==
  // count=0 do while m=N e=e–2*y if e=0 then puncture bit Cm Cm 2, from set S0 e=e+2*NC        
  // else if m%2==0 puncture bit C m from set S0 else if m%2==1 puncture bit Cm2, from set S0
  // end if m=m+1 end do if Ni NC ( ) 2 3 1 ≤ y=3*N-Ni e=N m=1 count=0 do while m=N e=e-2*y if
  // e=0 then if count %2==0 puncture bit Cm2, from set S0 endif if count %2==1 puncture bit  
  // Cm1, from set S0 endif e=e+2*NC count=count+1 end if m=m+1 enddo endif above algorithm  
  // follows turbo code puncturing rules imposed. 3GPP/TSG/RAN/WG1#4 TDOC 338/99 in above     
  // algorithm, NiNC 
  // =23 means code rate=1/2 optimal puncturing pattern of code rate 1/2 proposed     
  //    puncturing=    
  // algorithm provides same puncturing pattern. when NiNC 
  // 23 is transparent optimal puncturing pattern 1/2. Systematic bits Parity bits 1 Parity     
  // bits     
  // 2 
  // puncturing pattern=1/2 turbo code Simulation Results Simulation conditions are below. ● 
  // Interleaver depth is 640 ● Internal interleaver is CDI. ● Constraint length of the     
  // constituent code is 4. ● Conventional termination method is applied. ● A full MAP with     
  // floating point implementation is used for decoding of constituent encoders ● Iteration     
  // number   
  // is 4. ● At BER 10 5−, at least 100 frame errors have to be counted ● Simulations are     
  // carried out in an AWGN channel ● Conventional puncturing algorithm parameters Comparison     
  // performed Case 1 : 128 puncturing 1/2 turbo code Effective code rate=640640 2 12     
  // 12864011640     
  // 55.+−== Case 2 : 384 puncturing from 1/3 turbo code Effective code rate=640640 3 12     
  // 38464015480 41*.+−== The simulation results shows proposed puncturing algorithm coding     
  // gain=     
  // 0.04 dB at BER 10 5−and 0.015 dB at FER=10 3−in Case 1. In Case 2, proposed    
  // puncturing=     
  // algorithm coding gain of 0.1 dB at a BER of 10 5−and 0.07 dB at FER=     
  // 10−.3GPP/TSG/RAN/WG1#4 TDOC 338/99 1.000E-04 1.000E-03 1.000E-02 1.000E-01 1.000E+00     
  // Frame=     
  // and bit error rate comparison of 128 punctured=1/2 turbo code(Case 1) 1.000E-02 1.000E-01     
  // 1.000E+00 Frame and bit error rate comparison of 384 punctured 1/3 turbo code(Case 2)

To enhance the performance of the conventional puncturing algorithm for turbo code, a novel puncturing algorithm is proposed in which puncturing is only done alternatively between two encoder parity bits. The proposed puncturing algorithm is simple and has superior performance over conventional algorithms.[http://groups.google.com/group/sci.math/browse_thread/thread/22ca261e5b95cc6d#]⏎
⏎
==References==
<references/>
* Greenlaw, Raymond, James Hoover, and Walter Ruzzo. ''Limits To Parallel computation; P-Completeness Theory''. ISBN 0-19-508591-4
* Heribert Vollmer. ''Introduction to Circuit Complexity -- A Uniform Approach''. ISBN 3-540-64310-9
* {{cite book|author = [[Christos Papadimitriou]] | year = 1993 | title = Computational Complexity | publisher = Addison Wesley | edition = 1st edition | isbn = 0-201-53082-1}} Section 15.3: The class '''NC''', pp.375&ndash;381.
* {{cite book|author = [[Dexter Kozen]] | year = 2006 | title = Theory of Computation | publisher = Springer | isbn = 1-84628-297-7}} Lecture 12: Relation of ''NC'' to Time-Space Classes

{{ComplexityClasses}}

{{DEFAULTSORT:Nc (Complexity)}}
[[Category:Complexity classes]]
[[Category:Circuit complexity]]

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[[es:NC (clase de complejidad)]]
[[ko:NC (복잡도)]]
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[[ja:NC (計算複雑性理論)]]