Using bit recycling to reduce the redundancy in plurally parsable dictionaries

Tunstall proposed an efficient algorithm for constructing the optimal dictionary of any particular size to obtain a variable-to-fixed code. More accurately, the algorithm constructs the optimal uniquely parsable dictionary. In fact, Savari showed that, if one allows herself to consider plurally parsable dictionaries, better codes may be constructed. Savari found a class of plurally parsable dictionaries that outperform the Tunstall code for memoryless, highly skewed, binary sources. This work addresses the redundancy in plurally parsable dictionaries and proposes the use of bit recycling as the means to reduce this redundancy, extending the range of random binary sources that may benefit from a plurally parsable dictionary at the same time. We present a theoretical analysis that evaluates the performance of variable-to-fixed codes based on the Tunstall dictionary and ones based on plurally parsable dictionaries, using Savari´s coding on the one hand and coding with bit recycling on the other hand.