Binary run length encoding example
This is a follow-up to my previous blog postthere is also a follow-up: Any run-length encoding requires you to store the number of repetitions. Most binary run length encoding example languages represent integers using a fixed number of bits in binary format. For example, Java represents integers int using 32 bits. Thus, we have a simple optimization problem: In practice, it might be better to store the data in a byte-aligned way.
That is, you should be using 8, 16, 32 or 64 bits. Indeed, reading numbers represented using an arbitrary number of bits may involve a CPU processing overhead. If you use too few bits, some long runs will have to count as several small runs.
If you use too many bits, you are wasting storage. Unfortunately, determining on a case-by-case basis the best number of bits requires multiple scans of the data. It also implies added software complexity. For example, using 3 bits, you could only allow the counter values 1,2,16, 24, 32,, In this example, the sequence of bits is interpreted as the value 1, the sequence of bits as the value 2, the sequence as 16, and so on.
Determining the best codes implies that you must scan the data, compute the histogram of the counters, and then apply some optimization algorithm such as dynamic programming. The decoding speed might be slight slower as you need to look-up the codes from a table.
If you are willing to sacrifice coding and decoding speed, then you can represent the counters using universal codes. Thus, instead of using a fixed number of bits and optimizing the representation as in the quantized coding ideayou seek an optimal variable-length representation of the counters. With this added freedom, you can be much more efficient. The illustrate the idea behind variable-length codes, we consider Gamma codes: Thus, we use x bits to represent the number x. Fortunately, we can do much better than Gamma codes and represent the number x using roughly 2 log x bits with delta codes.
Binary run length encoding example we can represent binary run length encoding example number N -1 as a Gamma code using N -1 bits, and then store x modulo 2 N binary run length encoding example binary format using N -1 bits.
Thus, we can represent all numbers up to 2 N -1 using 2 N -2 bits. Unfortunately, the current breed of microprocessors are not kind to variable-length representations so the added compression is at the expense decoding speed. Continue with part 3. References and further reading: See also the slides of my recent talk Compressing column-oriented indexes. Thank you for the interesting post. I would note, however, that not all universal codes are born equal.
They are used in search engines and allow very fast decompression. In many cases it takes the same time as to read the data from disk sequentially. Seems to be very interesting. My recent experience has tought me that compression and speed are no longer related that way, and largely for that reason.
These modern architectural features can be made to reward, with execution speed, high density in data. It is up to the designer to get the density, as well as the logic, that lets the hardware deliver the speed. I say that with some conviction having just finished optimizing a fast decompressor for structured data. It uses canonical Huffman codes binary run length encoding example the data, and a compressed variation of J. During software optimization, time and time again, I was able to get further speed improvements by increasing the compression not only of the data, but also of the decoding data structures and their pointers.
It was the variable-length coding, binary run length encoding example much as any other design factor, that got me the information density I needed from the data to get the speed I needed from the system. In the end, that happened, I believe, primarily because the use of variable-length codes reduced the demand on a relatively slow path component, the system bus. Software optimization is not what it was years ago, and for me at least, neither are the relationships between compression and speed.
Daniel I have read the references on Chronos and Bits. It looks like one should use terms variable-bit and variable-byte methods very cautiously. It is also interesting that Huffman coding can binary run length encoding example sped up considerably by using special lookup tables. Glenn, My experience and a variety of experimental evaluations just check the reference given by the authorsay that in many cases more sophisticated compression methods introduce speed penalty.
In particular, variable-bit methods are usually slower but not alwaysthat variable-byte methods. The difference, however, is subtle. In many cases, obviously, better compression rates allows to avoid expensive cache misses and even more expensive disk reads. In those case, better compression is obviously a priority. It could go either way; so much depends on the specifics.
But the stangest thing is that so often I find myself increasing compression in order to increase speed, and winning! It was the variable-length coding, as much as any other design factor, that got me the information density I needed. Like, why using counters to spot peculiar points within an address range when you can use flags bitsinterleaved in data or not sparse bit maps.
Your email address will not be published. For more help see http: Skip to content My home page My papers My software. Storing counters using a binary run length encoding example number of bits Most programming languages represent integers using a fixed number of bits in binary format.
Using variable-length counters for optimal compression If you are willing to sacrifice coding and decoding speed, then you can represent the counters using universal codes. Itman Thank you for the great reference. I liked the Fixed Binary Codewords paper very much. Looks like it is worth reading, thanks. Leave a Binary run length encoding example Cancel binary run length encoding example Your email address will not be published.
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Run-length encoding RLE is a very simple form of lossless data compression in which runs of data that is, sequences in which the same data value occurs in many consecutive data elements are stored as a single data value and count, rather than as the original run.
Binary run length encoding example is most useful on data binary run length encoding example contains many such runs. Consider, for example, simple graphic images such as icons, line drawings, and animations.
It is not useful with files that don't have many runs as it could greatly increase binary run length encoding example file size. RLE may also be used to refer to an early graphics file format supported by CompuServe for compressing black and white images, but was widely supplanted by their later Graphics Interchange Format. RLE also refers to a little-used image format in Windows 3.
For example, consider a screen containing plain black text on a solid white background. There will be many long runs of white pixels in the blank space, and many short runs of black pixels within the text. A hypothetical scan linewith B representing a black pixel and W representing white, might read as follows:. With a run-length encoding RLE data compression algorithm applied to the above hypothetical scan line, it can be rendered as follows:.
The run-length code represents the original 67 characters in only While the actual format used for the storage of images is generally binary rather than ASCII characters like this, the principle remains the same. Even binary data files can be compressed with this method; file format specifications often dictate repeated bytes in files as padding space.
Run-length encoding can be expressed in multiple ways to accommodate data properties as well as additional compression algorithms. For instance, one popular method encodes run lengths for runs of two or more characters only, using an "escape" symbol to identify runs, or using the character binary run length encoding example as the escape, so that any time a character appears twice it denotes a run.
On the previous example, this would give the following:. This would be interpreted as a run of twelve Ws, a B, a run of twelve Ws, a binary run length encoding example of three Bs, etc. In data where runs are less frequent, this can significantly improve the compression rate.
One other matter is the application of additional compression algorithms. Even with the runs extracted, the frequencies of different characters may be large, allowing for further compression; however, if the run lengths are written in the file in the locations where the runs occurred, the presence of these numbers interrupts the normal flow and makes it harder to compress.
To overcome this, some run-length encoders separate the data and escape symbols from the run lengths, so that the two can be handled independently. Run-length encoding schemes were employed in the binary run length encoding example of television signals as far back as The ITU also describes a standard to encode run-length-colour for fax machines, known as T.