University of Warsaw Faculty of Mathematics , Informatics and Mechanics Marek Biskup

In compressed data a single bit error propagates because of the corruption of the decoder’s state. This work is a study of error resilience in compressed data and, in particular, of the recovery of as much data as possible after a bit error. It is focused on Huffman codes. In a message encoded with a Huffman code a bit error causes the decoder to lose synchronization with the coder. The error propagates because the codewords seen by the decoder are misaligned. In case of most Huffman codes the decoder eventually resynchronizes. Nevertheless, there is no a priori upper bound on the number of incorrectly decoded symbols. The work introduces two novel methods for limiting error propagation in Huffman codes to not more than L bits, L being a parameter. In one method it is assumed that the decoder knows its position in the encoded message, in the other, the position of the decoder may be unknown. The methods are based on synchronization of a decoder that starts at an arbitrary bit of the encoded data. They utilize the inherent tendency of Huffman codes to synchronize spontaneously and do not introduce any redundancy if such a synchronization takes place. Another new method for limiting error propagation, presented in this dissertation, can be used in a wide class of codes. The methods are applied to parallel decoding of Huffman data and are tested on Jpeg compression. Additionally, an algorithm for finding correct codeword’s alignment by a decoder that starts in the middle of a message encoded with normal Huffman coding is presented. Statistical synchronization of Huffman codes is related to synchronizing strings — strings that always resynchronize the decoder. It is shown that finding a synchronizing string for a code is equivalent to a finding a synchronizing string for some finite automaton. Černý conjecture for this class of automata is discussed and an upper bound on the length of the shortest synchronizing string is presented. It is supported by an efficient algorithm that checks if a code has a synchronizing string and, if so, constructs a synchronizing string achieving the bound. Two classes of codes with a long shortest synchronizing string are shown with an exact length of the shortest synchronizing string. Finally, two efficient algorithms for finding all the synchronizing codewords — synchronizing strings that are codewords — of a Huffman code are presented.