Huffman coding achieves within one bit of source entropy but scales poorly

Evidence

Huffman coding is optimal in that it gets the code rate within one bit of the source entropy. However, because bits only come in integer multiples the efficiency for small symbol sets is quite low. In MPEG_1 layer 3 cod­ ers, some symbols are Huffman coded as pairs to allow a greater coding efficiency. However, there is a practical limit to the size of a Huffman code because the computation and the tables blow up exponentially in size and so become unfeasible. A more subtle limitation is that, for large symbol sets, it becomes very difficult to gather enough symbol statistics data with sufficient accuracy to generate a Huffman code. — David Howard, Jamie Angus, coustics and Psychoacoustics, 2640

Related

• A data source’s entropy gives the minimum bits needed to encode it (similarity 0.84)
• Audio symbols with high probability carry less information and need fewer bits (similarity 0.83)
• Huffman coding builds comma-free variable-length codes that need no separators between words. (similarity 0.82)
• Arithmetic coding approaches source entropy better than table-based Huffman methods (similarity 0.81)
• Quantizer levels need not be powers of two when entropy coding is used (similarity 0.79)
• Entropy encoding maximizes information carried by each bit pattern (similarity 0.79)