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Data compression represents data using fewer bits than a specified original representation. The saving can reduce storage in a file system and reduce the number of bits sent through a communication channel. At a fixed transmission rate, fewer bits arrive sooner; this makes better use of a fixed transmission budget. Both the encoded data and the instructions needed to interpret them contribute to the size of a stored file.

There are two different promises. Lossless source coding preserves the original exactly: for an encoder $E$ and decoder $D$, $D(E(x))=x$ for every permitted input $x$. Thus $E$ must be an injective function. Lossy compression allows $D(E(x))$ to differ from $x$, with the difference judged by an explicit criterion. A program or numerical record may require exact recovery; a preview image may tolerate altered pixels in return for fewer bits.

The appeal of lossless source coding is that repetition can be described rather than copied. Run-length encoding says "repeat this value twelve times"; a prefix code can give more frequent symbols shorter descriptions. These are distinct ways to exploit structure, and neither promises savings for every input. Image compression supplies especially visible examples of both lossless source coding and lossy compression.

Claude E. Shannon's 1948 paper made the role of probability distributions precise. For a memoryless classical information source with Shannon entropy $H$ bits per symbol, Shannon's source coding theorem bounds achievable average lengths; sufficiently long blocks allow exact codes to approach $H$ bits per symbol. This is a statement about a specified source and average lengths, not a promise to shorten every message.^[ref]

A file format specifies how a binary string is interpreted: field order, field widths, permitted values and where decoding stops. A data compression comparison must include all fields required to recover the data.

Image compression applies data compression to pictures, usually represented by raster images. Nearby pixels often have related shades; an encoder can exploit that structure. A flat region invites run-length encoding, while lossy block averaging trades fine detail for fewer stored samples. The choice depends on whether exact pixel values matter and on the patterns in the image.

Lossless source coding recovers the encoded pixel values exactly, including sharp text or numerical image data. Lossy compression preserves an approximation and can remove features that later image processing might need. A visually smooth result is therefore a different promise from exact recovery. Neither method has a universal compression ratio: the chosen file format, its file header and the particular image all matter.

PNG is a real format with lossless source coding of its encoded image data. Its specified compression uses Deflate on reversibly filtered rows, rather than our toy RLE format. The lossy block averaging example is also a teaching format, not a description of PNG. A lossy preprocessing step followed by saving as PNG preserves the already changed pixels, not the earlier original.^[ref]