Oversampled filter banks (OFBs) provide an overcomplete representation of their input signal. This paper describes how OFBs can be considered as error-correcting codes acting on real or complex sequences, very much like classical binary convolutional codes act on binary sequences. The structured

Important inference problems in statistical physics, computer vision, error-correcting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems

Abstract- This paper deals with a new class of convolutional codes called Turbo-codes, whose performances in terms of Bit Error Rate (BER) are close to the SHANNON limit. The Turbo-Code encoder is built using a parallel concatenation of two Recursive Systematic Convolutional codes

We study two families of error-correcting codes defined in terms of very sparse matrices. "MN" (MacKay--Neal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties

output representations. This paper compares these three approaches to a new technique in which error-correcting codes are employed as a distributed output representation. We show that these output representations improve the generalization performance of both C4.5 and backpropagation on a wide range

The brachistochrone problem is to nd the curve between two points down which a bead will slide in the shortest amount of time, neglecting friction and assuming conservation of energy. To solve the problem, an integral is derived that computes the amount of time it would take a bead to slide down a given curve y(x). This integral is minimized over all possible curves and yields the di erential equation y(1+(y 0) 2) = k 2 asaconstraint for the minimizing function y(x). Solving this di erential equation shows that a cycloid (the path traced out by a point on the rim ofarolling wheel) is the solution to the brachistochrone problem. First proposed in 1696 by Johann Bernoulli, this problem is credited with having led to the development of the calculus of variations. The solution presented assumes knowledge of one-dimensional calculus and elementary di erential equations.

PAPER AWARD. Multipermutations appear in various applications in information theory. New applications such as rank modulation for flash memories and voting have suggested the need to consider error-correcting codes for multipermutations. The construction of codes is challenging when permutations

. The cumulated errors then make the genomic memory ephemeral at the time scale of geology. Only means intrinsic to the genome itself, taking the form of error-correcting codes, can ensure the genome permanency. According to information theory, they can achieve reliable communication over unreliable channels, so

. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery operator independent definition of error-correcting codes. We relate

There is a unique way to teach: to lead the other person through the same experience with which you learned. Óscar Villarroya, cognitive scientist. 1 In this book, the mathematical aspects in our presentation of the basic theory of block error-correcting codes go together, in mutual reinforcement