Methods for efficient bounded-distance decoding of the Hexacode

Details Methods for efficient bounded-distance decoding of the Hexacode Methods for efficient bounded-distance decoding of the Hexacode

1996-11-18

1998-09-08

Baker, Stephen M.

Excavating

371 3704, 371 3706, 371 3709, H03H 1300

Patent

active

058056130

ABSTRACT:
A method for bounded distance decoding of symbols received in transmission when the original symbols belonged to a Block code featuring series of symbols forming legitimate codewords whose metric distance from the received transmission is measured in Square Euclidean Distance (SED), when the maximum number of errors per word is upward bound by d-1; in which the Block code can be divided into subsets which will each define the entire codeword; and in which the maximum number of errors in at least one subset is one. The method includes dividing the received symbols into a number of blocks per codeword and decoding each block separately and simultaneously with regard to a maximum of one error present in each block. The solution of the decoder is the legitimate codeword with the lowest overall metric distance (SED) from the received transmission.

REFERENCES:
patent: 4731799 (1988-03-01), Longstaff et al.
patent: 4933956 (1990-06-01), Forney, Jr.
Amrani, O. et al, "Efficient Bounded-Distance Decoding of the Hexacode and Associated Decoders for the Leech Lattice and the Golay Code", IEEE Transactions on Communications, vol. 44, No. 5, pp. 534-537 (May 1996).
Amrani, O. et al, "The Leech Lattice and the Golay Code: Bounded-Distance Decoding and Multilevel Constructions", IEEE Transactions on Information Theory, vol. 40, No. 4, pp. 1030-1043, Jul. 1994.
Blahut, R.E., "Theory and Practice of Error Control Codes" pp. 1-15.
Sklar, B., "Digital Communications: Fundamentals and Applications" pp. 269-273.

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