From Code Design for Dependable Systems
9.1 ERROR LOCATION OF FAULTY PACKAGES AND FAULTY CHIPS
As was shown in Figure 1.11 in Subsection 1.4.1, error location falls midway between the
functions of error correction and error detection. In the codes designed by Wolf and Elspas,
the codeword is divided into p distinct bytes, each having b-bit length. The code detects
e(< b) or fewer errors, all occurring within a single byte and identifies that byte. For this
reason the code is referred to as the Single e-bit (within a b-bit byte) Error Locating code, or
Se/bEL code. For instance, if we let Ei(Ej) be the set of e or fewer errors occurring within the
i(j)-th byte, the code must satisfy the relation
The number of check bits r is bounded from below by
where [x] is the smallest integer not less than x.
In general, the error locating code is derived from the tensor product of the parity-check
Definition 9.1 Let the X = (xi, j) and Y = (yi, j...
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9.2 BLOCK ERROR LOCATING (Sb/p×bEL) CODES First, we study a class of block error locating codes that can locate an erroneous block containing a single-byte error. This is the Sb/p×b...
9.4 SINGLE-BIT ERROR CORRECTING AND SINGLE-BYTE ERROR LOCATING (SEC-Se=bEL) CODES We study here another class of error locating codes, namely Single-bit Error Correcting and Single e-bit...
9.3.4 Evaluation Error Detection Capabilities The SEC-Sb/p×bEL codes do not always detect random double-bit errors and also do not always detect double-byte errors. These errors...
9.3.2 Design for SEC-Sb/p×bEL Codes 1. Codes Designed by Tensor Product — Codes I — In general, we can design the error locating codes by means of the tensor product of two...
9.3 SINGLE-BIT ERROR CORRECTING AND SINGLE-BLOCK ERROR LOCATING (SEC-Sb/p×bEL) CODES This section deals with the SEC-Sb/p×bEL codes, where B = p × b that correct single-bit...