Properties of Optimal <i>k</i>-Bit Delay Decodable Alphabetic Codes

An alphabetic code is a source code that preserves the lexicographical order between sequences in the encoding process. This paper studies k-bit delay alphabetic code-tuples, which are alphabetic codes allowing multiple code tables and at most k-bit decoding delay. As the main results, we show theorems to limit the scope of codes to be considered when discussing k-bit delay alphabetic code-tuples with the optimal average codeword length in theoretical analysis and practical code construction. These theorems imply the existence of an optimal k-bit delay alphabetic code whose code tables are all injective. They also give an upper bound of the necessary number of code tables for an alphabetic code to be optimal. In addition to the results above for a general integer k ≥ 0, we prove further results for particular cases k = 1, 2.