Reliable information storage in memories designed from unreliable components

This is the first of two papers which consider the theoretical capabilities of computing systems designed from unreliable components. This paper discusses the capabilities of memories; the second paper discusses the capabilities of entire computing systems. Both present existence theorems analogous to the existence theorems of information theory. The fundamental result of information theory is that communication channels have a capacity, C, such that for all information rates less than C, arbitrarily reliable communication can be achieved. In analogy with this result, it is shown that each type of memory has an information storage capacity, C, such that for all memory redundancies greater than 1/C arbitrarily reliable information storage can be achieved. Since memory components malfunction in many different ways, two representative models for component malfunctions are considered. The first is based on the assumption that malfunctions of a particular component are statistically independent from one use to another. The second is based on the assumption that components fail permanently but that bad components are periodically replaced with good ones. In both cases, malfunctions in different components are assumed to be independent. For both models it is shown that there exist memories, constructed entirely from unreliable components of the assumed type, which have nonzero information storage capacities.