On a Two-Dimensional Antidictionary Coding

This paper proposes a new two-dimensional antidictionary coding for a given rectangle. An antidictionary is the set of all the minimal forbidden rectangles for an input rectangle. The proposed encoder outputs a pair of an antidictionary and a unique polyomino which appears only once in an input rectangle as a codeword. The input rectangle can be decoded from the pair. Both the encoding and decoding schemes do not require line-scanning and the neighbors of a decoded rectangle can be reproduced in an arbitrary order. Moreover, we show that there is a one-to-one correspondence between a rectangle and an antidictionary.