Data compression ratio: Difference between revisions
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{{Short description|Measurement of the power of a data compression algorithm}} | {{Short description|Measurement of the power of a data compression algorithm}} | ||
{{broader|Data compression}} | {{broader|Data compression}} | ||
'''Data compression ratio''', also known as '''compression power''', is a measurement of the relative reduction in size of data representation produced by a data compression algorithm. It is typically expressed as the division of uncompressed size by compressed size. | '''Data compression ratio''', also known as '''compression power''', is a measurement of the relative reduction in size of data representation produced by a data [[Data compression|compression algorithm]]. It is typically expressed as the division of uncompressed size by compressed size. | ||
==Definition== | ==Definition== | ||
Data compression ratio is defined as the ratio between the ''uncompressed size'' and ''compressed size'':<ref name=CompressionRatioBroadcastEngineering>{{cite news |title=Pixel grids, bit rate and compression ratio |publisher=Broadcast Engineering |url=http://broadcastengineering.com/storage-amp-networking/pixel-grids-bit-rate-and-compression-ratio |date=2007-12-01 |access-date=2013-06-05 |url-status=dead |archive-url=https://web.archive.org/web/20131010224651/http://broadcastengineering.com/storage-amp-networking/pixel-grids-bit-rate-and-compression-ratio |archive-date=2013-10-10 }}</ref><ref name="CompressionRatioDigitalVideoandHD">{{cite news|title=Digital Video and HD: Algorithms and Interfaces|author=Charles Poynton|date=2012-02-07|publisher=[[Morgan Kaufmann Publishers]]|edition=2nd|isbn=9780123919267|author-link=Charles Poynton}}<!--|accessdate=2013-06-05--></ref><ref name=CompressionRatioHEVCdraft10>{{cite news |title=High Efficiency Video Coding (HEVC) text specification draft 10 (for FDIS & Consent) |publisher=JCT-VC |url=http://phenix.it-sudparis.eu/jct/doc_end_user/current_document.php?id=7243 |date=2013-01-17 |access-date=2013-06-05}}</ref><ref name=CompressionRatioLogitechAVCStandard>{{cite news |title=The H.264 Advanced Video Coding (AVC) Standard |publisher=Logitech |url=http://www.logitech.com/assets/45120/logitechh.pdf |archive-url=https://web.archive.org/web/20130219161340/http://www.logitech.com/assets/45120/logitechh.pdf |archive-date=2013-02-19 |url-status=live |access-date=2013-06-05}}</ref><ref name=CompressionRatioSonyBroadcastApplications>{{cite news |title=White Paper on Performance Characteristics of MPEG-2 Long GoP vs AVC-I video compression techniques for Broadcast Applications |publisher=[[Sony]] |url=http://pro.sony.com/bbsccms/assets/files/micro/xdcam/solutions/MPEG-2_Long_GoP_vs_AVC_Comp-Strategies.pdf |archive-url=https://web.archive.org/web/20091229065501/http://pro.sony.com/bbsccms/assets/files/micro/xdcam/solutions/MPEG-2_Long_GoP_vs_AVC_Comp-Strategies.pdf |archive-date=2009-12-29 |url-status=live |access-date=2013-06-05}}</ref> | Data compression ratio is defined as the ratio between the ''uncompressed size'' and ''compressed size'':<ref name=CompressionRatioBroadcastEngineering>{{cite news |title=Pixel grids, bit rate and compression ratio |publisher=Broadcast Engineering |url=http://broadcastengineering.com/storage-amp-networking/pixel-grids-bit-rate-and-compression-ratio |date=2007-12-01 |access-date=2013-06-05 |url-status=dead |archive-url=https://web.archive.org/web/20131010224651/http://broadcastengineering.com/storage-amp-networking/pixel-grids-bit-rate-and-compression-ratio |archive-date=2013-10-10 }}</ref><ref name="CompressionRatioDigitalVideoandHD">{{cite news|title=Digital Video and HD: Algorithms and Interfaces|author=Charles Poynton|date=2012-02-07|publisher=[[Morgan Kaufmann Publishers]]|edition=2nd|isbn=9780123919267|author-link=Charles Poynton}}<!--|accessdate=2013-06-05--></ref><ref name=CompressionRatioHEVCdraft10>{{cite news |title=High Efficiency Video Coding (HEVC) text specification draft 10 (for FDIS & Consent) |publisher=JCT-VC |url=http://phenix.it-sudparis.eu/jct/doc_end_user/current_document.php?id=7243 |date=2013-01-17 |access-date=2013-06-05 |archive-date=2019-12-31 |archive-url=https://web.archive.org/web/20191231032724/http://phenix.it-sudparis.eu/jct/doc_end_user/current_document.php?id=7243 |url-status=dead }}</ref><ref name=CompressionRatioLogitechAVCStandard>{{cite news |title=The H.264 Advanced Video Coding (AVC) Standard |publisher=Logitech |url=http://www.logitech.com/assets/45120/logitechh.pdf |archive-url=https://web.archive.org/web/20130219161340/http://www.logitech.com/assets/45120/logitechh.pdf |archive-date=2013-02-19 |url-status=live |access-date=2013-06-05}}</ref><ref name=CompressionRatioSonyBroadcastApplications>{{cite news |title=White Paper on Performance Characteristics of MPEG-2 Long GoP vs AVC-I video compression techniques for Broadcast Applications |publisher=[[Sony]] |url=http://pro.sony.com/bbsccms/assets/files/micro/xdcam/solutions/MPEG-2_Long_GoP_vs_AVC_Comp-Strategies.pdf |archive-url=https://web.archive.org/web/20091229065501/http://pro.sony.com/bbsccms/assets/files/micro/xdcam/solutions/MPEG-2_Long_GoP_vs_AVC_Comp-Strategies.pdf |archive-date=2009-12-29 |url-status=live |access-date=2013-06-05}}</ref> | ||
:<math> {\rm Compression\;Ratio} = \frac{\rm Uncompressed\;Size}{\rm Compressed\;Size}</math> | :<math> {\rm Compression\;Ratio} = \frac{\rm Uncompressed\;Size}{\rm Compressed\;Size}</math> | ||
Compression Ratio = Uncompressed Size/Compressed Size | |||
Thus, a representation that compresses a file's storage size from 10 MB to 2 MB has a compression ratio of 10/2 = 5, often notated as an explicit ratio, 5:1 (read "five" to "one"), or as an implicit ratio, 5/1. This formulation applies equally for compression, where the uncompressed size is that of the original; and for decompression, where the uncompressed size is that of the reproduction. | Thus, a representation that compresses a file's storage size from 10 MB to 2 MB has a compression ratio of 10/2 = 5, often notated as an explicit ratio, 5:1 (read "five" to "one"), or as an implicit ratio, 5/1. This formulation applies equally for compression, where the uncompressed size is that of the original; and for decompression, where the uncompressed size is that of the reproduction. | ||
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:<math>{\rm Space\;Saving} = 1 - \frac{\rm Compressed\;Size}{\rm Uncompressed\;Size}</math> | :<math>{\rm Space\;Saving} = 1 - \frac{\rm Compressed\;Size}{\rm Uncompressed\;Size}</math> | ||
Space Saving = 1 - Compressed Size/Uncompressed Size | |||
Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%. | Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%. | ||
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:<math> {\rm Compression\;Ratio} = \frac{\rm Uncompressed\;Data\;Rate}{\rm Compressed\;Data\;Rate}</math> | :<math> {\rm Compression\;Ratio} = \frac{\rm Uncompressed\;Data\;Rate}{\rm Compressed\;Data\;Rate}</math> | ||
Compression Ratio = Uncompressed Data Rate/Compressed Data Rate | |||
and instead of space saving, one speaks of '''data-rate saving''', which is defined as the data-rate reduction relative to the uncompressed data rate: | and instead of space saving, one speaks of '''data-rate saving''', which is defined as the data-rate reduction relative to the uncompressed data rate: | ||
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:<math>{\rm Data\;Rate\;Saving} = 1 - \frac{\rm Compressed\;Data\;Rate}{\rm Uncompressed\;Data\;Rate}</math> | :<math>{\rm Data\;Rate\;Saving} = 1 - \frac{\rm Compressed\;Data\;Rate}{\rm Uncompressed\;Data\;Rate}</math> | ||
For example, uncompressed songs in CD format have a data rate of 16 bits/channel x 2 channels x 44.1 kHz ≅ 1.4 Mbit/s, whereas [[Advanced Audio Coding|AAC]] files on an iPod are typically compressed to 128 kbit/s, yielding a compression ratio of 10.9, for a data-rate saving of 0.91, or 91%. | Date Rate Saving = 1 - Compressed Data Rate/Uncompressed Data Rate | ||
For example, uncompressed songs in CD format have a data rate of 16 bits/channel x 2 channels x 44.1 [[Hertz|kHz]] ≅ 1.4 Mbit/s, whereas [[Advanced Audio Coding|AAC]] files on an iPod are typically compressed to 128 kbit/s, yielding a compression ratio of 10.9, for a data-rate saving of 0.91, or 91%. | |||
When the uncompressed data rate is known, the compression ratio can be inferred from the compressed data rate. | When the uncompressed data rate is known, the compression ratio can be inferred from the compressed data rate. | ||
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==Uses== | ==Uses== | ||
The data compression ratio can serve as a measure of the [[complexity]] of a data set or signal. In particular it is used to approximate the [[algorithmic information theory|algorithmic complexity]]. It is also used to see how much of a file is able to be compressed without increasing its original size. | The data compression ratio can serve as a measure of the [[complexity]] of a [[data set]] or signal. In particular it is used to approximate the [[algorithmic information theory|algorithmic complexity]]. It is also used to see how much of a file is able to be compressed without increasing its original size. | ||
==References== | ==References== | ||