A Lower Bound of Worst-Case Redundancy of $k$-Symbol Delay Decodable Codes

The class of $k$-symbol delay decodable code-tuples is a set of noiseless source codes, which can achieve an average codeword length less than or equal to that of Huffman codes by utilizing a finite number of code tables and allowing a decoding delay of at most $k$ coding symbols. This paper establishes a lower bound of the worst-case redundancy of $d$-ary $k$-symbol delay decodable code-tuples for $d \geq 2, k \geq 1$ by proving a stronger theorem that provides a lower bound of the average codeword length.