Tradeoffs on the volume of fault-tolerant circuits

Understand

Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation.

• Choosing an appropriate code is non-trivial as it must balance several requirements.
• Increasing the rate of the code reduces the relative number of redundant bits used in the fault-tolerant circuit, while increasing the distance of the code ensures robustness against faults.
• If the rate and distance were the only concerns, we could use asymptotically optimal codes as is done in communication settings.