An alternative to the Hamming code in the class of SEC-DED codes in semiconductor memory (original) (raw)
Related papers
SOME NEW RESULTS ON BINARY LINEAR BLOCK CODES
Certain properties of the parity-check matrix H of (n, k) linear codes are used to establish a computerised search procedure for new binary linear codes. Of the new error-correcting codes found by this procedure, two codes were capable of correcting up to two errors, three codes up to three errors, four codes up to four errors and one code up to five errors. Two meet the lower bound given by Helgert and Stinaff, and seven codes exceed it. In addition, one meets the upper bound. Of the even-Hamming-distance versions of these codes, eight meet the upper bound, and the remaining two exceed the lower bound.
Generalized Hamming weights of linear codes
IEEE Transactions on Information Theory, 1992
Error control codes are widely used to increase the reliability of transmission of information over various forms of communications channels. The Hamming weight of a codeword is the number of nonzero entries in the word; the weights of the words in a linear code determine the error-correcting capacity of the code. The r th generalized Hamming weight for a linear code C, denoted by d r (C), is the minimum of the support sizes for r-dimensional subcodes of C. For instance, d 1 (C) equals the traditional minimum Hamming weight of C. In 1991, Feng, Tzeng, and Wei proved that the second generalized Hamming weight d 2 (C) = 8 for all double-error correcting BCH(2 m , 5) codes. We study d 3 (C) and higher Hamming weights for BCH(2 m , 5) codes by a close examination of the words of weight 5. end:
Discrete Applied Mathematics, 2009
A binary linear code in F n 2 with dimension k and minimum distance d is called an [n, k, d] code. A t-(n, m, λ) design D is a set X of n points together with a collection of m-subsets of X (called a block) such that every t-subset of X is contained in exactly λ blocks. A constant length code which corrects different numbers of errors in different code words is called a non-uniform error correcting code. Parity sectioned reduction of a linear code gives a non-uniform error correcting code. In this paper a new code, [2 n − 1, n, 2 n−1 ], is developed. The error correcting capability of this code is 2 n−2 − 1 = e. It is shown that this code holds a 2-(2 n − 1, 2 n−1 , 2 n−2 ) design. Also the parity sectioned reduction code after deleting the same g (≤ e) positions of each code word of this code holds a 1-(
Generalized parity-check matrices for SEC-DED codes with fixed parity
2011
Hsiao and extended Hamming parity-check matrices can be used to define systematic linear block codes for Single Error Correction-Double Error Detection (SEC-DED). Their fixed code word parity enables the construction of low density parity-check matrices and fast hardware implementations. Fixed code word parity is enabled by an all-one row in extended Hamming paritycheck matrices or by the constraint that the modulo-2 sum of all rows is equal to the all-zero vector in Hsiao paritycheck matrices. In this paper, we show that these two constraints are particular instantiations of a more general constraint which involves an arbitrary number of rows in the parity-check matrix. As a consequence, sparser paritycheck matrices with faster hardware implementations can be found. Moreover, special instantiations of these matrices enable the detection of all triple-bit and quadruplebit burst errors.
Binary and ternary linear codes which are good and proper for error correction
All binary cyclic codes of lengths up to 31 and ternary cyclic and negacyclic codes of lengths up to 20 have been tested and those of them which satisfy the sufficient conditions to be good and proper for error correction have been determined. The same way some binary distance optimal linear codes of lengths up to 33 have been tested. Tables with the results have been prepared.
RAIRO - Theoretical Informatics and Applications, 2005
Motivated by a problem posed by Hamming in 1980, we define even codes. They are Huffman type prefix codes with the additional property of being able to detect the occurrence of an odd number of 1-bit errors in the message. We characterize optimal even codes and describe a simple method for constructing the optimal codes. Further, we compare optimal even codes with Huffman codes for equal frequencies. We show that the maximum encoding in an optimal even code is at most two bits larger than the maximum encoding in a Huffman tree. Moreover, it is always possible to choose an optimal even code such that this difference drops to 1 bit. We compare average sizes and show that the average size of an encoding in a optimal even tree is at least 1/3 and at most 1/2 of a bit larger than that of a Huffman tree. These values represent the overhead in the encoding sizes for having the ability to detect an odd number of errors in the message. Finally, we discuss the case of arbitrary frequencies and describe some results for this situation.
Optimal codes for single-error correction, double-adjacent-error detection
IEEE Transactions on Information Theory, 2000
In certain memory systems the most common error is a single error and the next most common error is two errors in positions which are stored physically adjacent in the memory. In this correspondence we present optimal codes for recovering from such errors. We correct single errors and detect double adjacent errors. For detecting adjacent errors we consider codes which are byte-organized. In the binary case, it is clear that the length of the code is at most 2 1, where is the redundancy of the code. We summarize the known results and some new ones in this case. For the nonbinary case we show an upper bound, called "the pairs bound," on the length of such code. Over GF (3) codes with bytes of size 2 which attain the bound exist if and only if perfect codes with minimum Hamming distance 5 over GF(3) exist. Over GF (4) codes which attain the bound with byte size 2 exist for all redundancies. For most other parameters we prove the nonexistence of codes which attain the bound.