We study two families of error-correcting codes defined in terms of very sparse matrices "MN" (MacKay-Neal (1995)) 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 The decoding of both codes can be tackled with a practical sum-product algorithm We prove that these codes are "very good", in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit This result holds not only for the binary-symmetric channel but also for any channel with symmetric stationary ergodic noise We give experimental results for binary-symmetric channels and Gaussian channels demonstrating that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed, the performance of Gallager codes is almost as close to the Shannon limit as that of turbo codes

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Good error-correcting codes based on very sparse matrices

ireless personal communications could in principle use several physical media, ranging from sound to radio to light. Since we want to overcome the limitations of acoustical com

Propagation Measurements and Models for Wireless Communications Channels To achieve ubiquitous PCS, new and novel ways of classifying wireless environments will be needed that are both widely encompassing and reasonably compact.

The authors describe the type of signals that occur in various environments and the modeling of the propagation parameters. Models are essentially of two classes. The first class consists of parametric statistical models that on average describe the phenomenon within a given error. They are simple to use, but relatively coarse. In the last few years a second class of environment-specific models has been introduced. These models are of a more deterministic nature, characterizing a specific street, building, etc. They are necessarily more time consuming to use, but are also more revealing concerning physical details and hopefully more accurate. Some key parameters and the measurement of them are discussed and then the different wireless environments are treated. The latter topic is divided into outdoor environments, indoor environments, and radio penetration from outdoor to indoor environments. >

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Propagation measurements and models for wireless communications channels

Frequency-selective fading caused by multipath time delay spread degrades digital communication channels by causing intersymbol interference, thus resulting in an irreducible BER and imposing a upper limit on the data symbol rate. In this paper, a frequencyselective, slowly fading channel is studied by computer simulation. The unfiltered BPSK, QPSK, OQPSK, and MSK modulations are considered first to illustrate the physical insights and the error mechanisms. Two classes of modulation with spectral-shaping filtering are studied next to assess the tradeoff between spectral occupancy and the performance under the influence of time delay spread. The simulation is very flexible so that different channel parameters can be studied and optimized either individually or collectively. The irreducible BER averaged over fading samples with a given delay profile is used to compare different modulation/detection methods, while the cumulative distribution of short-term BER is employed to show allowable data symbol rates for given values of delay spread. It is found that both GMSK and QPSK with a raised-cosine Nyquist pulse are suitable for a TDM/TDMA digital portable communications channel.

The Effects of Time Delay Spread on Portable Radio Communications Channels with Digital Modulation

The authors describe a system that combines the orthogonal frequency-division multiplexing technique and a coding strategy associated with diversity in the frequency domain. The system is suitable for digital broadcasting through a particularly hostile urban radio channel. The general principles of COFDM (coded orthogonal frequency-division multiplexing) are explained, and a detailed representation of the signals and the decoding procedure is given. The performance of the system in the selective Rayleigh channel is presented, and the behavior of the system when the conditions of temporal and frequency coherence of the channel are not fully met (very high-speed reception and abnormally extended channel delay spread) is described. The first implementation of a 4-PSK-COFDM systems has been demonstrated at the WARC-ORB 88 conference in Geneva, validating this concept of digital sound broadcasting. >

Digital sound broadcasting to mobile receivers

Binary unit memory codes, originally introduced by Lee, are investigated. A few examples of constant unit memory codes are given and bounds on the distance profile and the free distances are discussed. For time-varying codes asymptotic lower bounds on the distance profile and the free distance are given. The error probability for the codes, used on a memoryless binary-input, output-symmetric channel, is asymptotically upper bounded. The asymptotic results for the free distance and the error probability, which are in some respects better than for conventional convolutional codes, are interpreted by Forney's inverse concatenation construction.

Bounds on distances and error exponents of unit memory codes

Binary linear concatenated codes with Reed-Solomon codes as the outer code and varying nonsystematic inner codes are investigated. It is shown that codes exist in this class which asymptotically meet the Gilbert-Varshamov bound.

The existence of binary linear concatenated codes with Reed - Solomon outer codes which asymptotically meet the Gilbert- Varshamov bound

Recently Bleichenbacher et al. proposed a decoding algorithm for interleaved (N, K) Reed-Solomon codes, which allows close to N-K errors to be corrected in many cases. We discuss the application of this decoding algorithm to concatenated codes

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Decoding of concatenated codes with interleaved outer codes

The classical multipath model of mobile communications is reviewed and the importance of phase derivatives with respect to space and frequency is emphasised. Using an analogy it is shown that the group delay follows a Student's t-distribution, delay spread as the determining parameter, and does not depend on the details of the power delay profile. The delay spread is the second central moment of the average power delay profile. The distribution is important for frequency selective effects of datacommunication over a narrowband channel.

Christian Thommesen

Papers

Bounds on distances and error exponents of unit memory codes

The existence of binary linear concatenated codes with Reed - Solomon outer codes which asymptotically meet the Gilbert- Varshamov bound

Decoding of concatenated codes with interleaved outer codes

Distributions of Phase Derivatives in Mobile Communications

Decoding of concatenated codes with interleaved outer codes