A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j \geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.

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Low-Density Parity-Check Codes

This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver.

We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.

/pdf/on-limits-of-wireless-communications-in-a-fading-environment-2nxyevgur3.pdf

On Limits of Wireless Communications in a Fading Environment when UsingMultiple Antennas

The probability of error in decoding an optimal convolutional code transmitted over a memoryless channel is bounded from above and below as a function of the constraint length of the code. For all but pathological channels the bounds are asymptotically (exponentially) tight for rates above R_{0} , the computational cutoff rate of sequential decoding. As a function of constraint length the performance of optimal convolutional codes is shown to be superior to that of block codes of the same length, the relative improvement increasing with rate. The upper bound is obtained for a specific probabilistic nonsequential decoding algorithm which is shown to be asymptotically optimum for rates above R_{0} and whose performance bears certain similarities to that of sequential decoding algorithms.

Error bounds for convolutional codes and an asymptotically optimum decoding algorithm

This paper is a comparative study of feature selection methods in statistical learning of text categorization The focus is on aggres sive dimensionality reduction Five meth ods were evaluated including term selection based on document frequency DF informa tion gain IG mutual information MI a test CHI and term strength TS We found IG and CHI most e ective in our ex periments Using IG thresholding with a k nearest neighbor classi er on the Reuters cor pus removal of up to removal of unique terms actually yielded an improved classi cation accuracy measured by average preci sion DF thresholding performed similarly Indeed we found strong correlations between the DF IG and CHI values of a term This suggests that DF thresholding the simplest method with the lowest cost in computation can be reliably used instead of IG or CHI when the computation of these measures are too expensive TS compares favorably with the other methods with up to vocabulary reduction but is not competitive at higher vo cabulary reduction levels In contrast MI had relatively poor performance due to its bias towards favoring rare terms and its sen sitivity to probability estimation errors

A Comparative Study on Feature Selection in Text Categorization

An overview is presented of the medical image processing literature on mutual-information-based registration. The aim of the survey is threefold: an introduction for those new to the field, an overview for those working in the field, and a reference for those searching for literature on a specific application. Methods are classified according to the different aspects of mutual-information-based registration. The main division is in aspects of the methodology and of the application. The part on methodology describes choices made on facets such as preprocessing of images, gray value interpolation, optimization, adaptations to the mutual information measure, and different types of geometrical transformations. The part on applications is a reference of the literature available on different modalities, on interpatient registration and on different anatomical objects. Comparison studies including mutual information are also considered. The paper starts with a description of entropy and mutual information and it closes with a discussion on past achievements and some future challenges.

/pdf/mutual-information-based-registration-of-medical-images-a-4xrv2limmo.pdf

Mutual-information-based registration of medical images: a survey

A warning device associated with a rotatable body comprising means on the rotatable body for creating a magnetic field, a receiving coil on a relatively stationary member arranged such that upon rotation of the rotatable body interaction with the magnetic field causes electrical pulses to be generated in the receiving coil and an electronic switching circuit operated by the pulses such that a warning is given upon occurrence of a predetermined condition, such as pressure of a vehicle wheel deviating outside a predetermined limit.

W. T. Wintringham

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