The Trapping Redundancy of Linear Block Codes

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. ©...

Asymptotic Average Redundancy of Huffman (and Shannon-Fano) Block Codes

We study the redundancy of Huffman code (which, incidentally, is as old as the author of this paper). It has been known from the inception of this code that in the worst case Huffman code redundancy defined as the excess of the code length over the optimal (ideal) code length is not more than onc. Over more than forty years, insightful, elegant and useful constructions have been set up to deter...

Trellis decoding complexity of linear block codes

AbstructIn this partially tutorial paper, we examine minimal trellis representations of linear block codes and analyze several measures of trellis complexity: maximum state and edge dimensions, total span length, and total vertices, edges and mergers. We obtain bounds on these complexities as extensions of well-known dimensiodlength profile (DLP) bounds. Codes meeting these bounds minimize all ...

RNN Decoding of Linear Block Codes

Designing a practical, low complexity, close to optimal, channel decoder for powerful algebraic codes with short to moderate block length is an open research problem. Recently it has been shown that a feed-forward neural network architecture can improve on standard belief propagation decoding, despite the large example space. In this paper we introduce a recurrent neural network architecture fo...