A memory device includes a memory; and at least one processor configured to: obtain a symbol stream including a plurality of symbols; determine a Huffman tree corresponding to the symbol stream, wherein each symbol of the plurality of symbols is assigned a corresponding prefix code from among a plurality of prefix codes based on the Huffman tree; generate a prefix length table based on the Huffman tree, wherein the prefix length table indicates a length of the corresponding prefix code for each symbol; generate a logarithm frequency table based on the prefix length table, wherein the logarithm frequency table indicates a logarithm of a frequency count for each symbol, generate a cumulative frequency table which indicates a cumulative frequency count corresponding to each symbol; generate a compressed bitstream by iteratively applying an encoding function to the plurality of symbols based on the logarithm frequency table and the cumulative frequency table; and store the compressed bitstream in the memory.