Optical fiber networks currently transmit data at extremely high volumes, with error rates maintained at approximately 10^-10, meaning one erroneous bit per 1 GB of data. Industry trends suggest a performance growth pattern similar to Moore's Law, where transmission speeds triple every four years.
To increase data transmission rates, engineers focus on three primary methods: increasing the number of bits per symbol, raising the number of symbols transmitted per second, and utilizing multiple independent parallel channels. These approaches are constrained by the physical and theoretical limits of the communication medium.
Claude Shannon’s information theory defines information as a measure of uncertainty reduction. Entropy serves as the lower bound for the average number of binary questions required to identify a symbol. This mathematical framework establishes the theoretical limit for lossless data compression, where random sequences cannot be compressed further.
In real-world channels, noise and interference distort signals. The capacity of such a channel is determined by maximizing mutual information, which represents the difference between initial uncertainty and the residual uncertainty remaining after reception. This calculation accounts for the probability of errors occurring during transmission.
A binary symmetric channel illustrates these principles: if the error probability is 0, the channel transmits 1 bit of information per symbol. If the error probability is 11%, the mutual information drops to 0.5 bits per symbol. Predictability of errors is more critical than the mere presence of errors for maintaining transmission efficiency.
