A k-bit delay decodable code-tuple is a loss-less source code that can achieve a smaller average codeword length than Huffman codes by using a finite number of code tables and allowing at most k-bit delay for decoding. It is known that there exists a k-bit delay decodable code-tuple with at most 2(2k) - 2(2k-1 + 1)+1 code tables that attains the optimal average codeword length among all the k-bit delay decodable code-tuples for any given i.i.d. source distribution. Namely, it suffices to con- sider only the code-tuples with at most 2(2k) - 2(2k-1+1) + 1 code tables to accomplish optimality. In this paper, we propose a method to significantly reduce the number of code tables considered in the theoretical analysis, code construction, and coding processes by focusing on symmetry among code tables.
HASHIMOTO et al. (Thu,) studied this question.