Modulo-N code - Revision history

PragyaanRover at 13:07, 11 December 2024

2024-12-11T13:07:10Z

← Previous revision		Revision as of 13:07, 11 December 2024
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	When applied to two nodes in a [[computer networking\|network]] whose data are in close range of each other modulo-''N'' code requires one node (say odd) to send the coded data value as the raw data <math>M_o = D_o</math>; the even node is required to send the coded data as the <math> M_e = D_e \bmod N </math>. Hence the name modulo-''N'' code.		When applied to two nodes in a [[computer networking\|network]] whose data are in close range of each other modulo-''N'' code requires one node (say odd) to send the coded data value as the raw data <math>M_o = D_o</math>; the even node is required to send the coded data as the <math> M_e = D_e \bmod N </math>. Hence the name modulo-''N'' code.

	Since at least <math>\log_2 K</math> bits are required to represent a number ''K'' in binary, the modulo coded data of the two nodes requires <math>\log_2 M_o + \log_2 M_e</math> bits. As we can generally expect <math>\log_2 M_e \le \log_2 M_o</math> always, because <math>M_e \le N</math>. This is ~~the~~ how compression is achieved.		Since at least <math>\log_2 K</math> bits are required to represent a number ''K'' in binary, the modulo coded data of the two nodes requires <math>\log_2 M_o + \log_2 M_e</math> bits. As we can generally expect <math>\log_2 M_e \le \log_2 M_o</math> always, because <math>M_e \le N</math>. This is how compression is achieved.

	A compression ratio achieved is <math>\text{C.R.} = \frac{\log_2 M_o + \log_2 M_e}{2\log_2 M_o}.</math>		A compression ratio achieved is <math>\text{C.R.} = \frac{\log_2 M_o + \log_2 M_e}{2\log_2 M_o}.</math>

	==Decompression==		==Decompression==
	At the receiver by joint decoding we may complete the process of extracting the data and rebuilding the original values. The code from the even node is reconstructed by the ''assumption'' that it must be close to the data from the odd node. Hence the decoding algorithm retrieves even node data as		At the receiver, by joint decoding, we may complete the process of extracting the data and rebuilding the original values. The code from the even node is reconstructed by the ''assumption'' that it must be close to the data from the odd node. Hence the decoding algorithm retrieves even node data as

	: <math>\operatorname{CLOSEST}(M_o,N.k+ M_e).</math>		: <math>\operatorname{CLOSEST}(M_o,N.k+ M_e).</math>

Boleyn: has ref

2024-06-24T15:01:57Z

has ref

← Previous revision		Revision as of 15:01, 24 June 2024
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	* [[DISCUS]] is a more sophisticated technique for compressing correlated data sources.		* [[DISCUS]] is a more sophisticated technique for compressing correlated data sources.
	* [[Delta encoding]] is a related algorithm used in lossless compression algorithms designed for correlated data sources.		* [[Delta encoding]] is a related algorithm used in lossless compression algorithms designed for correlated data sources.

			==References==
			{{reflist}}

	{{DEFAULTSORT:Modulo-N Code}}		{{DEFAULTSORT:Modulo-N Code}}

Pass the pasta: #suggestededit-add 1.0

2022-01-29T18:09:32Z

#suggestededit-add 1.0

← Previous revision		Revision as of 18:09, 29 January 2022
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			{{Short description\|Lossy Compression Algorithm}}
	{{DISPLAYTITLE:Modulo-''N'' code}}		{{DISPLAYTITLE:Modulo-''N'' code}}
	{{Unreferenced\|date=December 2009}}		{{Unreferenced\|date=December 2009}}

Michael Hardy at 02:45, 20 February 2020

2020-02-20T02:45:08Z

← Previous revision		Revision as of 02:45, 20 February 2020
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			{{DISPLAYTITLE:Modulo-''N'' code}}
	{{Unreferenced\|date=December 2009}}		{{Unreferenced\|date=December 2009}}
	'''Modulo-''N'' code''' is a [[lossy compression]] algorithm used to compress [[correlated]] data sources using [[modular arithmetic]].		'''Modulo-''N'' code''' is a [[lossy compression]] algorithm used to compress [[correlated]] data sources using [[modular arithmetic]].

Michael Hardy: A lot of copy-editing was desperately needed here.

2020-02-20T02:44:27Z

A lot of copy-editing was desperately needed here.

← Previous revision		Revision as of 02:44, 20 February 2020
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	{{Unreferenced\|date=December 2009}}		{{Unreferenced\|date=December 2009}}
	'''Modulo-N code''' is a [[lossy compression]] algorithm used to compress [[correlated]] data sources using [[~~modulo~~ arithmetic]].		'''Modulo-''N'' code''' is a [[lossy compression]] algorithm used to compress [[correlated]] data sources using [[modular arithmetic]].

	==Compression==		==Compression==
	When applied to two nodes in a [[computer networking\|network]] whose data are in close range of each other ~~Modulo~~-N code		When applied to two nodes in a [[computer networking\|network]] whose data are in close range of each other modulo-''N'' code requires one node (say odd) to send the coded data value as the raw data <math>M_o = D_o</math>; the even node is required to send the coded data as the <math> M_e = D_e \bmod N </math>. Hence the name modulo-''N'' code.
	requires one node (say odd) to send the coded data value as the raw data <math>M_o = D_o</math>; the even node is required
	to send the coded data as the <math> M_e = (D_e) mod (N) </math>. Hence the name Modulo-N code.

			Since at least <math>\log_2 K</math> bits are required to represent a number ''K'' in binary, the modulo coded data of the two nodes requires <math>\log_2 M_o + \log_2 M_e</math> bits. As we can generally expect <math>\log_2 M_e \le \log_2 M_o</math> always, because <math>M_e \le N</math>. This is the how compression is achieved.
	Since it is known that for a number K, at least <math>log_2(K)</math> bits are required to represent it
	in binary. So the modulo coded data of the two nodes requires totally <math>log_2(M_o) + log_2(M_e)</math>.
	As we can generally expect <math>log_2(M_e) \le log_2(M_o)</math> always, because <math>M_e \le N</math>.
	This is the how compression is achieved.

	A compression ratio achieved is <math>C.R = \frac{log_2(M_o) + log_2(M_e)}{~~2log_2(~~M_o)}</math>.		A compression ratio achieved is <math>\text{C.R.} = \frac{\log_2 M_o + \log_2 M_e}{2\log_2 M_o}.</math>

	==Decompression==		==Decompression==
	At the receiver by joint decoding we may complete the process of extracting the data and rebuilding the		At the receiver by joint decoding we may complete the process of extracting the data and rebuilding the original values. The code from the even node is reconstructed by the ''assumption'' that it must be close to the data from the odd node. Hence the decoding algorithm retrieves even node data as
	original values. The code from the even node is reconstructed by the ''assumption'' that it must be
	close to the data from the odd node. Hence the decoding algorithm retrieves even node data as <BR />
⚫	<math>CLOSEST(M_o,N.k+ M_e)</math>.

		⚫	: <math>\operatorname{CLOSEST}(M_o,N.k+ M_e).</math>
⚫	The decoder essentially finds the closest match to <math>M_o \simeq N.k + M_e</math> and the decoded

	value is declared as <math>N.k + M_e</math>
		⚫	The decoder essentially finds the closest match to <math>M_o \simeq N.k + M_e</math> and the decoded value is declared as <math>N.k + M_e</math>

	==Example==		==Example==
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	D_o=43,D_e=47		D_o=43,D_e=47

	Modulo-N decoding is similar to [[phase unwrapping]] and has the same limitation: If the difference from one node to the next is more than N/2 (if the phase changes from one sample to the next more than <math>\pi</math>), then decoding leads to an incorrect value.		Modulo-''N'' decoding is similar to [[phase unwrapping]] and has the same limitation: If the difference from one node to the next is more than ''N''/2 (if the phase changes from one sample to the next more than <math>\pi</math>), then decoding leads to an incorrect value.

	===See also===		==See also==
	* [[DISCUS]] is a more sophisticated technique for compressing correlated data sources.		* [[DISCUS]] is a more sophisticated technique for compressing correlated data sources.
	* [[Delta encoding]] is a related algorithm used in lossless compression algorithms designed for correlated data sources.		* [[Delta encoding]] is a related algorithm used in lossless compression algorithms designed for correlated data sources.

Busukxuan: /* Example */ Changed "." (period) to "⋅" (\cdot in LaTeX)

2017-02-20T15:08:55Z

Example: Changed "." (period) to "⋅" (\cdot in LaTeX)

← Previous revision		Revision as of 15:08, 20 February 2017
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	''Decoder''		''Decoder''
	M_o=43,M_e=47 mod(8) = 7,		M_o=43,M_e=47 mod(8) = 7,
	D_o=43,D_e=CLOSEST(43,~~8.k~~ + 7)		D_o=43,D_e=CLOSEST(43,8⋅k + 7)
	<math> 43 \simeq 8.5 + 7</math>		<math> 43 \simeq 8 \cdot 5 + 7</math>
	D_o=43,D_e=47		D_o=43,D_e=47

Edward: link lossy compression using Find link

2015-08-05T17:31:18Z

link lossy compression using Find link

← Previous revision		Revision as of 17:31, 5 August 2015
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	{{Unreferenced\|date=December 2009}}		{{Unreferenced\|date=December 2009}}
	'''Modulo-N code''' is a lossy compression algorithm used to compress [[correlated]] data sources using [[modulo arithmetic]].		'''Modulo-N code''' is a [[lossy compression]] algorithm used to compress [[correlated]] data sources using [[modulo arithmetic]].

	==Compression==		==Compression==

Addbot: Bot: Removing Orphan Tag (Nolonger an Orphan) (Report Errors)

2013-01-09T02:43:41Z

Bot: Removing Orphan Tag (Nolonger an Orphan) (Report Errors)

← Previous revision		Revision as of 02:43, 9 January 2013
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	{{Unreferenced\|date=December 2009}}		{{Unreferenced\|date=December 2009}}
	{{Orphan\|date=December 2009}}

	'''Modulo-N code''' is a lossy compression algorithm used to compress [[correlated]] data sources using [[modulo arithmetic]].		'''Modulo-N code''' is a lossy compression algorithm used to compress [[correlated]] data sources using [[modulo arithmetic]].

SmackBot: remove Erik9bot category,outdated, tag and general fixes, added orphan tag

2009-12-16T22:49:54Z

remove Erik9bot category,outdated, tag and general fixes, added orphan tag

← Previous revision		Revision as of 22:49, 16 December 2009
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			{{Unreferenced\|date=December 2009}}
			{{Orphan\|date=December 2009}}

	'''Modulo-N code''' is a lossy compression algorithm used to compress [[correlated]] data sources using [[modulo arithmetic]].		'''Modulo-N code''' is a lossy compression algorithm used to compress [[correlated]] data sources using [[modulo arithmetic]].

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	Modulo-N decoding is similar to [[phase unwrapping]] and has the same limitation: If the difference from one node to the next is more than N/2 (if the phase changes from one sample to the next more than <math>\pi</math>), then decoding leads to an incorrect value.		Modulo-N decoding is similar to [[phase unwrapping]] and has the same limitation: If the difference from one node to the next is more than N/2 (if the phase changes from one sample to the next more than <math>\pi</math>), then decoding leads to an incorrect value.

	=== See also ===		===See also===
	* [[DISCUS]] is a more sophisticated technique for compressing correlated data sources.		* [[DISCUS]] is a more sophisticated technique for compressing correlated data sources.
	* [[Delta encoding]] is a related algorithm used in lossless compression algorithms designed for correlated data sources.		* [[Delta encoding]] is a related algorithm used in lossless compression algorithms designed for correlated data sources.

			{{DEFAULTSORT:Modulo-N Code}}
	[[Category:Information theory]]		[[Category:Information theory]]
	[[Category:Data compression]]		[[Category:Data compression]]
	[[Category:Articles lacking sources (Erik9bot)]]
	[[Category:Wireless sensor network]]		[[Category:Wireless sensor network]]

Erik9bot: add Category:Articles lacking sources (Erik9bot)

2009-08-27T18:36:53Z

add Category:Articles lacking sources (Erik9bot)

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	[[Category:Information theory]]		[[Category:Information theory]]
	[[Category:Data compression]]		[[Category:Data compression]]
			[[Category:Articles lacking sources (Erik9bot)]]
	[[Category:Wireless sensor network]]		[[Category:Wireless sensor network]]