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

Problems of Information Transmission

On Application of the Modulus Metric to Solving the Minimum Euclidean Distance Decoding Problem

Vyacheslav Davydov

Published Apr 1, 2019• 2 citations
Publisher

Abstract

We prove equivalence of using the modulus metric and Euclidean metric in solving the soft decoding problem for a memoryless discrete channel with binary input and Q -ary output. For such a channel, we give an example of a construction of binary codes correcting t binary errors in the Hamming metric. The constructed codes correct errors at the output of a demodulator with Q quantization errors as ( t + 1)( Q − 1) − 1 errors in the modulus metric. The obtained codes are shown to have polynomial decoding complexity.

DOI
10.1134/s0032946019020030

Related papers

Burst decoding of binary block codes on Q-ary output channels.

S. Wainberg, Jack K. Wolf

The burst-b distance between two binary vectors is defined and shown to be a metric. This definition is applied to a binary-input, Q-ary output channel where errors occur in bursts. A decoding algorithm is presented for such a channel that is an extension of Weldon's (1971) weighted erasure decoding. Examples are presented illustrating the techniques.

IEEE Transactions on Information Theory•Sep 1, 1972•17 citations

Euclidean distance soft-input soft-output decoding algorithm for low-density parity-check codes

Patrick Guy Farrell, Leonardo J. Arnone, Jorge Castiñeira Moreira

A new antilog–sum algorithm for decoding error-correcting codes is described. The soft-input, soft-output (SISO) algorithm uses squared Euclidean distance as the metric, does not require knowledge of the signal-to-noise ratio of the received signal and is less complex to implement than other SISO algorithms. The results of simulations show that the performance is very close to that of the log–sum–product algorithm.

IET Communications•Nov 4, 2011•13 citations

Weighted-Hamming Metric for Parallel Channels

Sebastian Bitzer, Alberto Ravagnani, Violetta Weger

Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-metric codes exhibit the unusual property that all errors beyond half the minimum distance can be corrected. Nevertheless, a tight relation between the error-correction capability of a code and its minimum distance can be established. Generalizing their Hamming-metric counterparts, upper and lower bounds on the cardinality of a code with a given weighted-Hamming distance are obtained. Finally, we propose a simple code construction with optimal minimum distance for specific parameters.

arXiv:2401.17801•IEEE International Symposium on Information Theory (ISIT)•Jul 7, 2024•1 citation

On the Optimality of the Hamming Metric for Decoding Block Codes over Binary Additive Noise Channels

Ghady Azar

Most of the basic concepts of algebraic coding theory are derived for the memoryless binary symmetric channel. These concepts do not necessarily hold for time-varying channels or for channels with memory. However, errors in real-life channels seem to occur in bursts rather than independently, suggesting that these channels exhibit some statistical dependence or memory. Nonetheless, the same algebraic codes are still commonly used in current communication systems that employ interleaving to spread channel error bursts over the set of received codewords to make the channel appear memoryless to the block decoder. This method suffers from immediate shortcomings as it fails to exploit the channel’s memory while adding delay to the system. We study optimal maximum likelihood block decoding of binary codes sent over several binary additive channels with infinite and finite memory. We derive conditions on general binary codes and channels parameters under which maximum likelihood and minimum distance decoding are equivalent. The channels considered in this work are the infinite and finite memory Polya contagion channels [1],

•Jan 1, 2013•1 citation

Algebraic analog decoding of linear binary codes

L. Rudolph, Carlos R. P. Hartmann, Tai-Yang Hwang +1 more

Bit-by-bit soft-decision decoding of binary cyclic codes is considered. A significant reduction in decoder complexity can be achieved by requiring only that the decoder correct all analog error patterns which fall within a Euclidean sphere whose radius is equal to half the minimum Euclidean distance of the code. Such a "maximum-radius" scheme is asymptotically optimum for the additive white Gaussian noise (AWGN) channel. An iterative extension of the basic algebraic analog decoding scheme is discussed, and performance curves are given for the (17,9), (21,11), and (73,45) codes on the AWGN channel.

IEEE Transactions on Information Theory•Jul 1, 1979•21 citations

A Soft-Input Soft-Output Decoding Algorithm for LDPC Codes

Lixin Wang

A new soft-input,soft-output algorithm for decoding LDPC codes is described in this paper.Using soft squared Euclidean distance as the metric,the algorithm realizes decoding by iterating the antilog-sum of the Euclidean distance.A simplified algorithm is also put forward to reduce computational complexity.The proposed algorithm does not require knowledge of the signal-to-noise ratio of the received signal and is less complex to implement than other soft decision algorithms.The results of simulation show that the performance is very close to that of sum-product algorithm while the computational complexity is sharply reduced.

Journal of Spacecraft TT&C Technology•Jan 1, 2011•0 citations
We prove equivalence of using the modulus metric and Euclidean metric in solving the soft decoding problem for a memoryless discrete channel with binary input and Q -ary output. For such a channel, we give an example of a construction of binary codes correcting t binary errors in the Hamming metric. The constructed codes correct errors at the output of a demodulator with Q quantization errors as ( t + 1)( Q − 1) − 1 errors in the modulus metric. The obtained codes are shown to have polynomial decoding complexity.
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-metric codes exhibit the unusual property that all errors beyond half the minimum distance can be corrected. Nevertheless, a tight relation between the error-correction capability of a code and its minimum distance can be established. Generalizing their Hamming-metric counterparts, upper and lower bounds on the cardinality of a code with a given weighted-Hamming distance are obtained. Finally, we propose a simple code construction with optimal minimum distance for specific parameters.
Most of the basic concepts of algebraic coding theory are derived for the memoryless binary symmetric channel. These concepts do not necessarily hold for time-varying channels or for channels with memory. However, errors in real-life channels seem to occur in bursts rather than independently, suggesting that these channels exhibit some statistical dependence or memory. Nonetheless, the same algebraic codes are still commonly used in current communication systems that employ interleaving to spread channel error bursts over the set of received codewords to make the channel appear memoryless to the block decoder. This method suffers from immediate shortcomings as it fails to exploit the channel’s memory while adding delay to the system. We study optimal maximum likelihood block decoding of binary codes sent over several binary additive channels with infinite and finite memory. We derive conditions on general binary codes and channels parameters under which maximum likelihood and minimum distance decoding are equivalent. The channels considered in this work are the infinite and finite memory Polya contagion channels [1],
Bit-by-bit soft-decision decoding of binary cyclic codes is considered. A significant reduction in decoder complexity can be achieved by requiring only that the decoder correct all analog error patterns which fall within a Euclidean sphere whose radius is equal to half the minimum Euclidean distance of the code. Such a "maximum-radius" scheme is asymptotically optimum for the additive white Gaussian noise (AWGN) channel. An iterative extension of the basic algebraic analog decoding scheme is discussed, and performance curves are given for the (17,9), (21,11), and (73,45) codes on the AWGN channel.
A new soft-input,soft-output algorithm for decoding LDPC codes is described in this paper.Using soft squared Euclidean distance as the metric,the algorithm realizes decoding by iterating the antilog-sum of the Euclidean distance.A simplified algorithm is also put forward to reduce computational complexity.The proposed algorithm does not require knowledge of the signal-to-noise ratio of the received signal and is less complex to implement than other soft decision algorithms.The results of simulation show that the performance is very close to that of sum-product algorithm while the computational complexity is sharply reduced.