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2014-01-29T15:21:31Z

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An '''Optical DPSK demodulator''' is a device that provides a method for converting an optical [[differential phase-shift keying]] (DPSK) signal to an intensity-keyed signal at the receiving end in [[fiber-optic communication]] networks. It is also known as [[delay line interferometer]] (DLI), or simply called '''DPSK demodulator'''.<ref>[http://www.optoplex.com/DPSK_Demodulator.htm DPSK demodulation for fiber-optic communications]</ref><ref>[http://216.234.124.74/ITFLabs/Products.php?locale=en&Line_no=13&sub_category_id=155&cat_category_id=138 All-Fiber Delay line interferometer and Optical DPSK demodulator]</ref>

[[Image:DPSK-Demodulation.gif|thumb|488px|right|Working principle of optical DPSK demodulation: (a) Incoming DPSK signal with uniform intensity, (b) 1-bit delay of the incoming DPSK signal with uniform intensity, and (c) Demodulated intensity signal after interference between (a)/(a') and (b)/(b').]]

The DPSK decoding method is achieved by comparing the [[Phase (waves)|phase]] of two sequential bits. An incoming DPSK optical signal is first split into two beams with equal intensities, in which one beam is delayed in space by an [[optical path difference]] that introduces a [[time delay]] corresponding to ''one bit''. The two beams in the two paths are then coherently recombined to [[Interference (wave propagation)|interfere]] each other constructively or destructively. The interference intensity is measured and becomes the intensity-keyed signal. A typical optical system for such a purpose is [[Mach-Zehnder interferometer]] or [[Michelson interferometer]], forming an optical DPSK Demodulator.

Delay time depends on the [[Bit rate|data rate]]. For instance, in a 40 Gbit/s system, one bit corresponds to 25 picoseconds, and light travels 5 mm in a [[fiber optics]] or 7.5 mm in [[free space]] within that period. Thus the optical path difference between the two beams is 5 mm or 7.5 mm depending on the type of interferometer used.

[[DQPSK]]<ref>[http://www.optoplex.com/DQPSK_Demodulator.htm DQPSK Demodulators]</ref><ref>[http://www.kylia.com/dpsk.html Tunable DPSK demodulator for DQPSK application]</ref> is the four-level version of DPSK. DQPSK transmits two bits for every symbol (bit combinations being 00, 01, 11 and 10) and has an additional advantage over conventional binary DPSK. DQPSK has a narrower optical spectrum, which tolerates more dispersion (both chromatic and polarization-mode), allows for stronger optical filtering, and enables closer channel spacing. As a result, DQPSK allows processing of 40 Gbit/s data-rate in a 50 GHz channel spacing system. A demodulator for optical DQPSK signals can be constructed using two matched DPSK demodulators with phase off-set at <math>\pm \pi/4</math>.

==References==

<references/>

{{DEFAULTSORT:DPSK demodulator, optical}}
[[Category:Fiber-optic communications]]
[[Category:Photonics]]

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2013-09-25T18:17:16Z

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{{redirect|SUHA|other uses|Suha (disambiguation){{!}}Suha}}
In [[computer science]], '''SUHA''' ('''S'''imple [[Uniform distribution (discrete)|'''U'''niform]] '''H'''ashing '''A'''ssumption) is a basic assumption that facilitates the mathematical analysis of [[Hash_Table|hash tables]]. The assumption states that a hypothetical [[hashing function]] will evenly distribute items into the slots of a hash table. Moreover, each item to be hashed has an equal [[probability]] of being placed into a slot, regardless of the other elements already placed. This assumption generalizes the details of the hash function and allows for certain assumptions about the stochastic system.

==Applications==
SUHA is most commonly used as a foundation for mathematical proofs describing the properties and behavior of hash tables in [[theoretical computer science]]. Minimizing [[Hash_collision|hashing collisions]] can be achieved with a uniform hashing function. These functions often rely on the specific input data set and can be quite difficult to implement. Assuming uniform hashing allows hash table analysis to be made without exact knowledge of the input or the hash function used.

==Mathematical implications==
Certain properties of hash tables can be derived once uniform hashing is assumed.

===Uniform distribution===
Under the assumption of uniform hashing, given a hash function '''''h''''', and a hash table of size '''''m''''', the probability that two non-equal elements will hash to the same slot is
:<math>P(h(a) = h(b)) = \frac{1}{m}.</math>

===Collision chain length===
Under the assumption of uniform hashing, the [[load factor (computer science)|load factor]] <math>\alpha</math> and the [[Average_case|average]] chain length of a hash table of size '''''m''''' with '''''n''''' elements will be
:<math>\alpha = \tfrac{n}{m}</math>

===Successful lookup===
Under the assumption of uniform hashing, the average time (in [[Big O notation|big-O notation]]) to successfully find an element in a hash table using [[Hash_table#Separate_chaining|chaining]] is
:<math>\Theta(\alpha + 1)\,</math>

===Unsuccessful lookup===
Under the assumption of uniform hashing, the average time (in big-O notation) to unsuccessfully find an element in a hash table using chaining is
:<math>\Theta(\alpha + 1)\,</math>

==Example==
A simple example of using SUHA can be seen while observing an arbitrary hash table of size 10 and a data set of 30 unique elements. If chaining is used to deal with collisions, the average chain length of this hash table may be a desirable value. Without any assumptions and with no more additional information about the data or hash function, the chain length cannot be estimated. With SUHA however, we can state that because of an assumed uniform hashing, each element has an equal probability of mapping to a slot. Since no particular slot should be favored over another, the 30 elements should hash into the 10 slots uniformly. This will produce a hash table with, on average, 10 chains each of length 3
:<math>\alpha = \tfrac{n}{m}</math>

:<math>\alpha = \tfrac{30}{10}</math>

:<math>\alpha = 3\,</math>

==See also==
*[[Hash Table]]
*[[Hash_collision|Hash Collision]]
*[[Perfect Hashing]]

==References==
===General===
* {{cite book
| last = Collins
| first = William
| title = Data Structures and the Java Collections Framework
| publisher = McGraw-Hill
| date= 2004
| chapter = Section 14.3.2: The Uniform Hashing Assumption
| pages = 608
| id = ISBN 0-07-282379-8 }}
* {{cite book
| last = Cormen
| first = Thomas H.
| authorlink = Thomas H. Cormen
| coauthors = [[Charles E. Leiserson]], [[Ronald L. Rivest]], [[Clifford Stein]]
| title = [[Introduction to Algorithms]]
| publisher = MIT Press and McGraw-Hill
| date= 2001
| chapter = Section 11.2: Hash Tables
| pages = 226–228
| id = ISBN 0-262-03293-7 }}

[[Category:Hashing]]

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