Intro to Channel Capacity (Information Theory)

The information content of a symbol equals log₂(M) bits, where M is the number of distinguishable signal levels—quantifying capacity gains from multi-level signaling.

Communication engineers have three primary dimensions for capacity enhancement: increasing symbol rate (baud), increasing levels per symbol (modulation), and sharing channels (multiplexing).

Thomas Edison developed the quadruplex telegraph applying multi-level signaling to Morse code systems, using four voltage levels: +3V, +1V, -1V, -3V, increasing telegraph capacity.

Edison’s quadruplex telegraph provided enormous economic value to Western Union by dramatically increasing message throughput without building new telegraph lines—infrastructure cost savings drove multi-level signaling adoption.

Multi-level signaling evolved from Edison’s four-voltage-level quadruplex through sophisticated modern schemes like 256-QAM using hundreds of distinguishable states, continuously pushing information density.

Beyond increasing symbol rate (baud), communication capacity can be enhanced by increasing the number of distinguishable signaling events—using multiple signal levels rather than simple on-off binary.

Claude Shannon’s 1948 channel capacity theorem establishes the maximum rate at which information can be reliably transmitted through a noisy channel: C = B log₂(1 + S/N), where B is bandwidth, S is signal power, N is noise power.

Increasing signal levels improves capacity but demands higher signal-to-noise ratio—noise limits practical number of distinguishable levels, creating fundamental capacity-reliability tradeoffs.

Alice and Bob discover that varying pluck characteristics—hardness (amplitude) and pitch (frequency)—enables faster string communication by encoding more information per signal.

Combining current direction (polarity) with intensity (amplitude) creates rich signaling vocabularies—Edison’s quadruplex used four voltage levels across positive and negative polarities.