Information Theory

Information theory is an academic field whose starting point is the paper "A Mathematical Theory of Communication," published by Claude Shannon in 1948. It quantified the amount of information in a unit called the bit, and mathematically clarified the limits of data compression and the maximum rate at which data can be sent without errors over a noisy channel (channel capacity).

The results of information theory are put to use in many places in the design of QR codes. From the standpoint of data compression, the QR code selects the optimal encoding mode according to the type of input data, such as numeric / alphanumeric / kanji, and maximizes storage efficiency. Numeric data alone takes about 3.3 bits per character and alphanumeric data about 5.5 bits, so efficient encoding is performed based on the statistical properties of the data.

From the standpoint of error correction, an error-correcting code called the Reed-Solomon code is adopted. This is a result of coding theory, a branch of information theory, and at error correction level H it achieves the ability to restore data even when up to about 30% of the data (codewords) is missing. The QR code embodies, at a practical level, the theorem Shannon showed: "even with noise, communication without errors is theoretically possible."