From Code Design for Dependable Systems

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 (within a b-bit byte) Error Locating codes, or SEC-Se/bEL codes.



9.4.1   Code Conditions and Bounds

Let Es be the error set consisting of all single-bit errors, and let Ei(Ej) be the set of e
or fewer bits errors in the i( j)-th byte excluding single-bit errors, where e < b and b is
the byte length. Thus Ei Ç Es = Ej Ç Es = φ for all ij, where f is the empty set. The
following theorem describes the necessary and sufficient conditions that characterize
SEC-Se/bEL codes.

Theorem 9.10   A linear code, described by the parity-check matrix H, corrects all
errors in Es and locates all errors in Ei, or Ej , where i ≠ j, if and only if:

where HT means the transpose of H.

Proof   It is apparent that conditions 1 and...


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Topics of Interest

9.4.2 Design for SEC-Se/bEL Codes The tensor product of the error correcting codes and the error detecting codes is also applied in the design of SEC-Se/bEL codes. That is, tensor product of an SbEC...

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...

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...

9.4.3   Evaluation Code Length   Figure 9.9 illustrates the relation between the information-bit length and the check-bit length of the SEC-Se/8EL codes for e = 2 and 6. In the figure the...

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...