Fault Detection Capacity of Code-Abiding Sample Clauses

Fault Detection Capacity of Code-Abiding. Permutations The protection offered by code embedding is that faults in the computation of the permutation are likely to lead to a decoding error. A decoding error implies that a fault occurred, but the converse is not necessarily true. If faults lead to an incorrect output that decodes successfully, we speak of undetected faults. In order to analyze more precisely the fault detection capacity of code-abiding permutations, we use a single-limb fault model. A single-limb fault, also simply called single fault, is a fault that modifies the value of only one limb. If imple- mented correctly, a single fault in the computation of a code-abiding permuta- tion is guaranteed to give a decoding error. To establish this, we analyze what happens when single faults are injected in a limb adaptation and transposition. A limb transposition either involves no computation at all or a correcting adaptation. In the latter case a single fault would only modify the value of one parity limb, while leaving the native limbs unchanged. The corresponding parity equation would then be not satisfied and decoding would fail. In a limb adaptation, fresh computations of φ are added to a native limb and one or more parity limbs. If the input of the limb adaptation is correct, it can only lead to an incorrect output that decodes successfully if at least d limbs are computed incorrectly, i.e. in the presence of d single faults, with d the distance of the code. At first sight, this is an argument for taking C with high distance