Go back to publications View external

Communication in the Presence of Noise

January 1949 C.E. Shannon Proceedings of the IRE, Vol. 37, No. 1, pp. 10-21
#Information Theory #Noise #Coding Theory

Abstract

This paper extends the basic theory to the practical problem of communicating in the presence of noise. It introduces the revolutionary concept that perfect (error-free) communication is possible, given sufficient redundancy in the encoding.

The Revolutionary Insight

Previously, engineers believed that to reduce errors, you had to reduce transmission rate. I showed that there exists a “channel capacity” - a rate below which you can communicate with arbitrarily small error probability by using sufficiently clever coding.

Key Results

Channel Capacity with Noise

For a channel with bandwidth W and signal-to-noise ratio S/N:

C=Wlog⁡2(1+S/N)C = W \log_2(1 + S/N)

This is the famous Shannon-Hartley theorem.

Error Correction Coding

The paper introduced the concept of:

  • Redundant encoding: Adding extra symbols to detect/correct errors
  • Code distance: Measuring error-correcting capability
  • Sphere packing: Geometric interpretation of coding

Practical Impact

This paper directly led to:

  • Turbo codes (used in 3G/4G mobile)
  • LDPC codes (used in WiFi, digital TV)
  • Reed-Solomon codes (CDs, DVDs, storage)
  • All modern error correction

The proof that we could communicate perfectly over imperfect channels changed everything.