Monday, October 19, 2009

Notes on Elias Gamma encoding in BitMagic 3.6.0

Version 3.6.0 implements a variant of Elias Gamma Encoding as part of bit-vector serialization.
Wikipedia has an article on this encoding here:

The description is so good that one should be able to implement this encoding after reading a couple of pages.

Older versions of BM library used D-Gap compression which is a variant of run length encoding. Or used plain lists of integers to encode very sparse sets. All this compression methods used word aligned algorithms and rely on presence of long runs of identical bits. Word aligned compression is also very fast.

A lot of practical tests demonstrated that BM based search systems are bandwidth limited. It means that CPU is starved, waiting for memory operations or disk retrieval. Disk retrieval is particularly important because IO and network subsystems never followed terms of Moore Law. Non-Word-Aligned encoding seems to a good answer to this problem.

Elias Gamma encoding developed by Peter Elias postulates bit-encoding of positive (non-zero) integers . Positive non-zero integers are essentially the native format for BM library to store sparse bit-vectors or inverted lists (basic building blocks of efficient bitmap indexes).

1.Simple implementation, requires no compression dictionary. It is easy to compress just a few ints without constructing and storing a dictionary. BM library works with independent blocks of bits (potentially computed in parallel).
2.Implied probability favors small integers – good for BM library since it fragments bit-vector into blocks of 65K bits. Methods allows some blocks to be encoded, and some to remain in GAP or raw bit-block format (if statistical distribution of bits suddenly changes).
3.Compact implementation reduces code bloat, fits into a C++ template library paradigm.

1.True adaptive statistical methods (like arithmetic compression) can(should?) give better compression ratio.
2.Encoding and decoding method is sequential, it seems hard to implement a parallel encoder/decoder using SIMD, SSE or GP-GPU. (BM blocks can potentially be decoded in parallel so maybe there is a way to use parallel methods for this).

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