Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Information Theory

One-step weighted-majority decoding (Corresp.)

L. Rudolph, Woodrow E. Robbins

Published May 1, 1972• 9 citations
Publisher

Abstract

It is shown that any decoding function for a linear binary code can be realized as a weighted majority of nonorthogonal parity checks. An example is given of a four-error-correcting code that is neither L-step orthogonalizable nor one-step majority decodable using non-orthogonal parity checks and yet is one-step weighted-majority decodable using only ten nonorthogonal parity checks.

DOI
10.1109/tit.1972.1054807

Related papers

Majority decoding the nonorthogonal parity checks (Corresp.)

Chin-Long Chen

A new bound on the error-correcting capability of majority decoding using nonorthogonal parity checks is derived. The new bound is then applied to a class of Euclidean geometry codes.

IEEE Transactions on Information Theory•Nov 1, 1976•1 citation

Further results on majority-logic decoding of product codes (Corresp.)

Nguyen Quang Đuc, L.V. Skattebol

In this correspondence additional results on majority-logic decoding of product codes are presented. If one of the component codes is decodable using Rudolph's nonorthogonal algorithm, and the other using Reed-Massey'sL-step orthogonalization, then the resulting product code is majority-logic decodable inLsteps, where nonorthogonal checks are used in the first step and orthogonal checks in the remaining steps. If the component codes are both decodable using Rudolph's algorithm, the product code is majority-logic decodable using the same procedure.

IEEE Transactions on Information Theory•Mar 1, 1972•1 citation

One-step majority-logic decoding with symbol reliability information (Corresp.)

C.-E.W. Sundberg

A method of using reliability information in one-step majority-logic decoders is presented. The idea is, basically, that the received binary digits are corrected in an order such that the least reliable digit is first corrected. With this method the error correction capability of the decoder is extended for large signal-to-noise ratios (SNR's). Different decoding algorithms are used when the number of orthogonal parity-check sums are even and odd, respectively. Computer simulations are presented for some short codes with binary antipodal signals on the additive white Gaussian noise channel.

IEEE Transactions on Information Theory•Mar 1, 1975•12 citations

On the Lin-Weldon majority-logic decoding algorithm for product codes (Corresp.)

Nguyen Quang Đuc

It is shown that a majority-logic decoding algorithm proposed by Lin and Weldon for the product of anL-step and a one-step orthogonalizable code is incomplete whenLis greater than unity. An improvement is presented to overcome this disadvantage in the binary case.

IEEE Transactions on Information Theory•Jul 1, 1973•2 citations

Graph theoreticq-ary codes (Corresp.)

L.S. Bobrow, S. L. Hakimi

This correspondence formulatesGF(q)matrix descriptions for a class of weighted, directed graphs. As a result of this formulation, the concept of graph theoretic error-correcting codes is generalized to theq-ary case. It is shown that graph theoreticq-ary codes are completely orthogonalizable and, hence, one-step majority decodable. It is also seen that known techniques for the augmentation of circuit codes can he extended to theq-ary case. The resulting codes remain easily decodable.

IEEE Transactions on Information Theory•Mar 1, 1971•7 citations

A note on one-step majority-logic decodable codes (Corresp.)

Chin-Long Chen, W. J. Warren

Construction of shortened geometric codes as Shown here results in 1-step majority-logic deeodable codes. The shortened codes retain the error-correction ability of the parent codes and the decoders for the shortened codes are much simpler than for the parent code. A table of shortened codes is given.

IEEE Transactions on Information Theory•Jan 1, 1973•2 citations
It is shown that any decoding function for a linear binary code can be realized as a weighted majority of nonorthogonal parity checks. An example is given of a four-error-correcting code that is neither L-step orthogonalizable nor one-step majority decodable using non-orthogonal parity checks and yet is one-step weighted-majority decodable using only ten nonorthogonal parity checks.
In this correspondence additional results on majority-logic decoding of product codes are presented. If one of the component codes is decodable using Rudolph's nonorthogonal algorithm, and the other using Reed-Massey'sL-step orthogonalization, then the resulting product code is majority-logic decodable inLsteps, where nonorthogonal checks are used in the first step and orthogonal checks in the remaining steps. If the component codes are both decodable using Rudolph's algorithm, the product code is majority-logic decodable using the same procedure.
A method of using reliability information in one-step majority-logic decoders is presented. The idea is, basically, that the received binary digits are corrected in an order such that the least reliable digit is first corrected. With this method the error correction capability of the decoder is extended for large signal-to-noise ratios (SNR's). Different decoding algorithms are used when the number of orthogonal parity-check sums are even and odd, respectively. Computer simulations are presented for some short codes with binary antipodal signals on the additive white Gaussian noise channel.