Recent Developments in Majority-Logic Decoding

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-67-C-0199Rome Air Development Center / F 30602-70-C-001

Some new results on majority-logic codes for correction of random errors

The main advantages of random error-correcting majority-logic codes and majority-logic decoding in general are well known and two-fold. Firstly, they offer a partial solution to a classical coding theory problem, that of decoder complexity. Secondly, a majority-logic decoder inherently corrects many more random error patterns than the minimum distance of the code implies is possible. The solution to the decoder complexity is only a partial one because there are circumstances under which a majority-logic decoder is too complex and expensive to implement. [Continues.

L-Step Majority Logic Decoding

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB 07-67-C-0199Rome Air Development Center / F30602-70-C-0014 (EMKC

On threshold decoding of cyclic codes

Bose-Chaudhuri-Hocquenghem (BCH) codes are very powerful random error-correcting techniques. We have investigated whether all BCH codes can be L-step orthogonalized, and have found a specific class of double error-correcting BCH codes which cannot be L-step orthogonalized. We show further that all BCH codes with length qm − 1, where q is a power of any prime p(q = p8), and all Euclidean geometry codes, can be one-step decoded by parity checks to correct a significant number of errors. These parity vectors need not be orthogonal to each other. For the general case, we have not been able to determine whether they can or cannot be decoded to their minimum distances by such a technique. The above codes decoded by nonorthogonal parity checks in the manner given herein are comparable to projective geometry codes, decoded by Rudolph's method