Showing papers on "BCH code published in 1974"
TL;DR: Two new infinite families of nonlinear binary codes are defined, which are called dual as their distance distributions satisfy the MacWilliams identities.
Abstract: A description is given of two new infinite families of nonlinear binary codes. For all block lengths n = 22m, m ≥ 3, two nonlinear binary codes are defined, which are called dual as their distance distributions satisfy the MacWilliams identities. The first code has minimum distance 8 and has four times as many codewords as the corresponding extended BCH code. In the other code, there are only six distinct nonzero values for the distances between codewords.
32 citations
TL;DR: In this article, a decoding method based on Berlekamp's iterative algorithm is presented which makes use of the multiple sets of syndrome sequences for decoding such cyclic codes beyond the BCH bound.
Abstract: Many cyclic codes are generated by polynomials possessing more than one set of consecutive roots. Thus more than one set of syndrome sequences are available for decoding. In this correspondence, a decoding method based on Berlekamp's iterative algorithm is presented which makes use of the multiple sets of syndrome sequences for decoding such cyclic codes beyond the BCH bound.
16 citations
TL;DR: In this article, a construction of cyclic codes in which an inner cyclic code is concatenated with appropriately chosen outer cyclic codewords is presented, and an example of the construction that improves on BCH codes of low rate is provided.
Abstract: A construction of cyclic codes in which an "inner" cyclic code is concatenated with appropriately chosen "outer" cyclic codes is presented. An example of the construction that improves on BCH codes of low rate is provided. Conversely, any cyclic code of length n_1 n_2 can be constructed by this construction, where n_1 and n_2 are relatively prime.
8 citations
TL;DR: The evaluation indicates that both encoding and decoding, for voice grade data communication facilities, can be done in contemporary communication processors with core storage in the 1000 word range and instruction cycles in the microsecond range.
Abstract: A general purpose communication processor is investigated as a vehicle for decoding two specific classes of cyclic codes having properties appropriate for voice grade data communication channels. First, a model of a processor is described, and then it is used in conjunction with two cost metrics to measure the complexity of programming the decoding functions. No special Galois field (GF) arithmetic instructions are used. For decoding both Bose-Chadhuri-Hocquenghem (BCH) and Fire codes, a method which allows the encoding program to be used in the initial steps of decoding is given and evaluated. The evaluation indicates that both encoding and decoding, for voice grade data communication facilities, can be done in contemporary communication processors with core storage in the 1000 word range and instruction cycles in the microsecond range. In addition, the results show how the cost metrics vary with parameters such as the block length, the number of errors or the burst length correctable, and the block error probability introduced by the channel. Other conclusions, such as the areas in which significant improvements are needed and in which hardware assist can improve performance are drawn from data giving the relative costs of the elements of the decoding process.
3 citations
TL;DR: This paper presents majority-decoding algorithms for four classes of binary cyclic codes for which the parity-check polynomial is the product of two primitive polynomials with relatively prime exponents, together with the corresponding nonexpurgated codes.
Abstract: This paper presents majority-decoding algorithms for four classes of binary cyclic codes. The classes are those for which the parity-check polynomial is: 1) the product of two primitive polynomials with relatively prime exponents and 2) the product of (x^r + 1)/(x + 1) and a primitive polynomial, where r \geq 3 is odd and the exponents are relatively prime, together with the corresponding nonexpurgated codes.
2 citations
01 Oct 1974
TL;DR: The hybrid scheme is shown to need less transmitter power than systems using either pure forward error correction or decision feedback with error detection alone, although the ability to reject error bursts is retained.
Abstract: Forward error correction (f.e.c.) and decision feedback (a.r.q.) are combined using a hybrid decoding scheme of partial error correction and partial error detection. This is shown to have advantages when a low error probability is required and efficient use of transmitter power is important. The performance of the scheme is analysed, assuming transmission over a channel disturbed primarily by white Gaussian noise. Results are presented for systems employing various BCH codes showing the effects on system performance of varying code length, code ratio, and of varying the maximumerror weight the decoder is allowed to correct. The hybrid scheme is shown to need less transmitter power than systems using either pure forward error correction or decision feedback with error detection alone, although the ability to reject error bursts is retained. A design procedure for choosing the code parameters and maximum error-correcting weight is given, and one method of implementing the decoding is suggested.
1 citations