Reduced Precision Redundancy for Reliable Processing of Data

Information is an integral part of the correct and reliable operation of today's computing systems. Data either stored or provided as input to computation processing modules must be tolerant to many externally and internally induced destructive phenomena such as soft errors and faults, often of a transient nature but also in large numbers, thus causing catastrophic system failures. Together with error tolerance, reliable operation must be provided by reducing the large overheads often encountered at system-level when employing redundancy. While information-based techniques can also be used in some of these schemes, the complexity and limited capabilities for implementing high order correction functions for decoding limit their application due to poor performance; therefore,
N
Modular Redundancy (
N
MR) is often employed. In
N
MR the correct output is given by majority voting among the
N
input copies of data. Reduced Precision Redundancy (RPR) has been advocated to reduce the redundancy, mostly for the case of
$N= 3$
; in a 3RPR scheme, one full precision (FP) input is needed while two inputs require reduced precision (RP) (usually by truncating some of the least significant bits (LSBs) in the input data). However, its decision logic is more complex than a 3MR scheme. This paper proposes a novel
N
RPR scheme with a simple comparison-based approach; the realistic case of
$N= 5$
is considered as an example to explain in detail such proposed scheme; different arrangements for the redundancy (with three or four FP data copies) are considered. In addition to the design of the decision circuit, a probabilistic analysis is also pursued to determine the conditions by which RPR data is provided as output; it is shown that its probability is very small. Different applications of the proposed
N
RPR system are presented; in these applications, data is used either as memory output and/or for computing the discrete cosine transform. In both cases, the proposed 5RPR scheme shows considerable advantages in terms of redundancy management and reliable image processing.