Delta encoding

Not to be confused with Elias delta coding.

Delta encoding is a way of storing or transmitting data in the form of differences between sequential data rather than complete files; more generally this is known as data differencing. Delta encoding is sometimes called delta compression, particularly where archival histories of changes are required (e.g., in revision control software).

The differences are recorded in discrete files called "deltas" or "diffs", after the Unix file comparison utility, diff. In situations with often small – for example, changing a few words in a large document, or changing a few records in a large table – delta encoding greatly reduces data redundancy. Collections of unique deltas are substantially more space-efficient than their non-encoded equivalents.

From a logical point of view the difference between two data values is the information required to obtain one value from the other – see relative entropy. The difference between identical values (under some equivalence) is often called 0 or the neutral element.

Simple example

Perhaps the simplest example is storing values of bytes as differences (deltas) between sequential values, rather than the values themselves. So, instead of 2, 4, 6, 9, 7, we would store 2, 2, 2, 3, −2. This is not very useful when used alone, but it can help further compression of data in which sequential values occur often. IFF 8SVX sound format applies this encoding to raw sound data before applying compression to it. Unfortunately, not even all 8-bit sound samples compress better when delta encoded, and the usability of delta encoding is even smaller for 16-bit and better samples. Therefore, compression algorithms often choose to delta encode only when the compression is better than without. However, in video compression delta frames can considerably reduce frame size, and are used in virtually every video compression codec.

Definition

A delta can be defined in 2 ways, symmetric delta and directed delta. A symmetric delta can be expressed as:

Δ(v₁, v₂) = (v₁ \ v₂) U (v₂ \ v₁),

where v₁ and v₂ represent two successive versions.

A directed delta, also called a change, is a sequence of (elementary) change operations which, when applied to one version v₁, yields another version v₂ (note the correspondence to transaction logs in databases).

Variants

A variation of delta encoding which encodes differences between the prefixes or suffixes of strings is called incremental encoding. It is particularly effective for sorted lists with small differences between strings, such as a list of words from a dictionary.

Implementation issues

The nature of the data to be encoded influences the effectiveness of a particular compression algorithm. For example, in sending updates to the Google Chrome browser, a specialized algorithm is used based on knowledge of the archive and executable format.

Delta encoding performs best when data has small or constant variation; for an unsorted data set, there may be little to no compression possible with this method.

In delta encoded transmission over a network where only a single copy of the file is available at each end of the communication channel, special error control codes are used to detect which parts of the file have changed since its previous version. For example, rsync uses a rolling checksum algorithm based on Mark Adler's adler-32 checksum.

Sample C code

The following C code performs a simple form of delta encoding and decoding:

void
delta_encode (char *buffer, const unsigned int length)
{
 char delta = 0;
 char original;
 unsigned int i;
 for (i = 0; i < length; ++i)
 {
  original = buffer[i];
  buffer[i] -= delta;
  delta = original;
 }
}

void
delta_decode (char *buffer, const unsigned int length)
{
 char delta = 0;
 unsigned int i;
 for (i = 0; i < length; ++i)
 {
  buffer[i] += delta;
  delta = buffer[i];
 }
}

Examples

Delta encoding in HTTP

Another instance of use of delta encoding is RFC 3229, "Delta encoding in HTTP", which proposes that HTTP servers should be able to send updated Web pages in the form of differences between versions (deltas), which should decrease Internet traffic, as most pages change slowly over time, rather than being completely rewritten repeatedly:

This document describes how delta encoding can be supported as a compatible extension to HTTP/1.1.

Many HTTP (Hypertext Transport Protocol) requests cause the retrieval of slightly modified instances of resources for which the client already has a cache entry. Research has shown that such modifying updates are frequent, and that the modifications are typically much smaller than the actual entity. In such cases, HTTP would make more efficient use of network bandwidth if it could transfer a minimal description of the changes, rather than the entire new instance of the resource.

Online backup

Main article: Online backup services

Many of the online backup services adopt this methodology, often known simply as deltas, in order to give their users previous versions of the same file from previous backups. This reduces associated costs, not only in the amount of data that has to be stored as differing versions (as the whole of each changed version of a file has to be offered for users to access), but also those costs in the uploading (and sometimes the downloading) of each file that has been updated (by just the smaller delta having to be used, rather than the whole file).

VCDIFF

Main article: VCDIFF

One general format for delta encoding is VCDIFF, described in RFC 3284. Free software implementations include Xdelta and open-vcdiff.

GDIFF

Generic Diff Format (GDIFF) is another delta encoding. It is submitted to W3C in 1997. In many cases, VCDIFF has better compression rate than GDIFF.

Diff

Main article: Diff

Diff is a file comparison program, which is mainly used for text files.

bsdiff

Bsdiff is a binary diff program using suffix sorting.

See also

• String-to-string correction problem
• Data differencing
• Source Code Control System
• Xdelta: open-source delta encoder

External links

• RFC 3229 – Delta Encoding in HTTP