A method for the construction of minimum-redundancy codes

@article{Huffman1952AMF,
  title={A method for the construction of minimum-redundancy codes},
  author={David A. Huffman},
  journal={Resonance},
  year={1952},
  volume={11},
  pages={91-99}
}
  • D. Huffman
  • Published 1 September 1952
  • Computer Science, Business
  • Resonance
SummaryAn optimum method of coding an ensemble of messages consisting of a finite number of members is developed. A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized. 

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References

SHOWING 1-2 OF 2 REFERENCES

A device for quantizing, grouping, and coding amplitude-modulated pulses

Thesis (M.S.) Massachusetts Institute of Technology. Dept. of Electrical Engineering, 1949.

A mathematical theory of communication, BellSys

  • Tech-J.,
  • 1948