Data compression ratio

Data compression ratio, also known as compression power, is a computer science term used to quantify the reduction in data-representation size produced by a data compression algorithm. The data compression ratio is analogous to the physical compression ratio used to measure physical compression of substances.

Definitions

Data compression ratio is defined as the ratio between the uncompressed size and compressed size:

$\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}=\frac{\mathrm{U}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}$

Thus a representation that compresses a 10MB file to 2MB 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. Note that 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.

Sometimes the space savings is given instead, which is defined as the reduction in size relative to the uncompressed size:

$\mathrm{S}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{S}\mathrm{a}\mathrm{v}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}=1-\frac{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}{\mathrm{U}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}$

Thus a representation that compresses a 10MB file to 2MB would yield a space savings of 1 - 2/10 = 0.8, often notated as a percentage, 80%.

For signals of indefinite size, such as streaming audio and video, the compression ratio is defined in terms of uncompressed and compressed data rates instead of data sizes:

$\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}=\frac{\mathrm{U}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}}$

and instead of space savings, one speaks of data-rate savings, which is defined as the data-rate reduction relative to the uncompressed data rate:

$\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{S}\mathrm{a}\mathrm{v}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}=1-\frac{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}}{\mathrm{U}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}}$

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 AAC files on an iPod are typically compressed to 128 kbit/s, yielding a compression ratio of 10.9, for a data-rate savings of 0.91, or 91%.

When the uncompressed data rate is known, the compression ratio can be inferred from the compressed data rate.

Lossless vs. lossy

Lossless compression of digitized data such as video, digitized film, and audio preserves all the information, but can rarely do much better than 2:1 compression because of the intrinsic entropy of the data. In contrast, lossy compression (for example JPEG, or MP3) can achieve much higher compression ratios at the cost of a decrease in quality, as visual or audio compression artifacts from loss of important information are introduced. A compression ratio of at least 50:1 is needed to get 1080i video into a 20 Mbit/s MPEG transport stream.

Uses

The data compression ratio can serve as an measure of the complexity of a data set or signal, in particular it is used to approximate the algorithmic complexity.

External links

• Nondegrading lossy compression