The optimal sequence compression

This paper presents the optimal compression for sequences with undefined values. Let we have (N -m) undefined and m defined positions in the boolean sequence V of length N. The sequence code length can't be less then m in general case, otherwise at least two sequences will have the same code. We present the coding algorithm which generates codes of almost m length, i.e. almost equal to the lower bound. The paper presents the decoding circuit too. The circuit has low complexity which depends from the inverse density of defined values D( V ) = N m . The decoding circuit includes RAM and random logic. It performs sequential decoding. The total RAM size is proportional to the log " D( V ) " , the number of random logic cells is proportional to log log " D( V ) " " log log log " D( V ) ""2 . So the decoding circuit will be small enough even for the very low density sequences. The decoder complexity doesn't depend of the sequence length at ...

• Type: Conference
• Year: 2006
• Where: DAGSTUHL
• Authors: Alexander E. Andreev
• Keywords: DAGSTUHL 2006, DAGSTUHL 2007, Random Logic, Sequence Code Length, Undefined Values