Linear Block Codes for Four-Dimensional Signals

Binary Linear Block Codes

Linear error-block codes

A linear error-block code is a natural generalization of the classical error-correcting code and has applications in experimental design, high-dimensional numerical integration and cryptography. This article formulates the concept of a linear error-block code and derives basic results for this kind of code by direct analogy to the classical case. Some problems for further research are raised. ©...

Neural Network Decoders for Linear Block Codes

This paper presents a class of neural networks suitable for the application of decoding error-correcting codes.The neural model is basically a perceptron with a high-order polynomial as its discriminant function. A single layer of high-order perceptrons is shown to be able to decode a binary linear block code with at most 2 weights in each perceptron, where m is the parity length. For some subc...

Trellis Representations for Linear Block Codes

Trellis Representations for Linear Block Codes Heide Gluesing-Luerssen University of Kentucky Department of Mathematics 715 Patterson Office Tower Lexington, KY 40506 USA During the last decade conventional and tail-biting trellis representations of linear block codes have gained a great deal of attention. A tail-biting trellis for a block code of length n is an edge-labeled layered graph on th...

Voronoi regions for binary linear block codes

The Voronoi regions of a block code govern many aspects of the code’s performance on a Gaussian channel, and they are fundamental instruments in, for example, error probability analysis and soft decision decoding. This paper presents an efficient method to find the boundaries of the Voronoi regions for an arbitrary binary linear block code. Two theoretical results together lead to the Voronoi r...