Error Errore Eicitur: A Stochastic Resonance Paradigm for Reliable Storage of Information on Unreliable Media

Abstract

Abstract-We give an architecture of a storage system consisting of a storage medium made of unreliable memory elements and an error correction circuit made of a combination of noisy and noiseless logic gates that is capable of retaining the stored information with lower probability of error than a storage system with a correction circuit made completely of noiseless logic gates. Our correction circuit is based on iterative decoding of low-density parity check codes, and uses the positive effect of errors in logic gates to correct errors in memory elements. In the spirit of Marcus Tullius Cicero's "Clavus clavo eicitur," ("one nail drives out another") the proposed storage system operates on the principle: "Error errore eicitur" -"one error drives out another." The randomness that is present in the logic gates makes these classes of decoders superior to their noiseless counterparts. Moreover, random perturbations do not require any additional computational resources as they are inherent to unreliable hardware itself. To utilize the benefits of logic gate failures, our correction circuit relies on two key novelties: a mixture of reliable and unreliable gates and decoder rewinding. We present a method based on absorbing Markov chains for the probability of error analysis, and explain how the randomness in the variable and check node update function helps a decoder to escape to local minima associated with trapping sets.

Hard-decision decoding of LDPC codes under timing errors: Overview and new results

“…In contrary to a popular beliefs that hardware failures have negative impact on decoding, in our previous work we showed that deliberate failure insertion can be beneficial to the decoding process [20]- [22]. We attributed such behaviour to stochastic resonance, a phenomenon well exploited in neural systems, semiconductor and quantum devices.…”

“…This surprising effect we first observed in the case of von Neumann failures [20], [39] and showed that message perturbations caused by gate failures can help decoder to escape from trapping sets. Furthermore, in the infinite number of iterations all trapping sets break, and the decoding process always converge to a valid codeword.…”

Recent Advances on Stochastic and Noise Enhanced Methods in Error Correction Decoders

“…In the same year, Noisy Gradient Descent Bit Flipping (NGDBF) was described for the Gaussian channel [9] and the related Probabilistic Gradient Descent Bit Flipping (PGDBF) algorithm for the BSC [10]. These works led to a number of algorithm and hardware improvements for NGDBF [11]- [13] and PGDBF [14]- [17], along with potential specialized applications in solid-state storage [18]. A related approach, known as the Improved Differential Binary (IDB) decoder, was also proposed in 2014 [19].…”

Stochastic resonance decoding for quantum LDPC codes

“…A decoder with such rewinding schedule is referred to as the rewind-decoder. Optimization of the parameter r is discussed in [12], and is code dependent. Example 1 (Breaking Four-Cycle): We now illustrate an example of how the stochastic Gallager-B algorithm escapes from a 4-cycle trapping set.…”

“…The use of stochastic resonance enables the decoder to escape from trapping sets and converge to a codeword. This idea introduced in the context of classical codes [12] can be naturally extended to the quantum decoding paradigm. Similar to noisy classical gates resulting from technology shrinkage and low supply voltages within the mesoscopic physical regime, the state-of-the-art quantum logic gates using photonics have fidelities that are approximately 0.91 [13].…”