From Code Design for Dependable Systems


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
matrices [WOLF65a].

Definition 9.1   Let the X = (xi, j) and Y = (yi, j...

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Error Correction Chips
Error correction chips are semiconductor ICs that are used to check and to correct data transmission errors.
Parity Checkers and Generators
Parity checkers are integrated circuits (ICs) used in digital systems to detect errors when streams of bits are sent from a transmitter to a receiver. Parity generators calculate the parity of data packets and add a parity amount to them.
Memory Modules
Memory modules are computer chips used to add memory to a computer.
FLASH Memory Chips
FLASH memory chips offer extremely fast access times, low power consumption, and relative immunity to severe shock or vibration. They do not need a constant power supply to retain their data. 
Memory Chips
Memory chips are internal storage areas in computers. Although the term "memory chip" commonly refers to a computer's random access memory (RAM), this product area includes many different types of electronic data storage. Computer memory stores data electronically in cells. Without memory chips, a computer could not read programs or retain data.

Topics of Interest

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...