Christian Thommesen

Bounds on distances and error exponents of unit memory codes

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 Forneys inverse concatenation construction.

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

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.

Statistics of phase derivatives in mobile communications

For high signal-to noise ratios the channel quality is limited by phase variations in frequency and space. The probability distributions of group delay, Doppler shift, and bandwidth have been found, and for the two former it is a Students t-distribution. The probability distributions depend only on the first and second moments of power profiles, not on the details of the distribution of scatterers. Implications for signal transmission are discussed briefly.

Concatenated codes with fixed inner code and random outer code

We derive lower bounds on the distance and error exponent of the coding scheme described in the title. The bounds are compared to the parameters and error performance of a concatenated code family with varying inner codes of equal rates and a fixed minimum-distance separable (MDS) code as the outer code, letting the inner and outer code lengths approach infinity.

Concatenated codes with convolutional inner codes

The minimum distance of concatenated codes with Reed-Solomon outer codes and convolutional inner codes is studied. For suitable combinations of parameters the minimum distance can be lower-bounded by the product of the minimum distances of the inner and outer codes. For a randomized ensemble of concatenated codes a lower bound of the Gilbert-Varshamov type is proved. >

On the feng-rao bound for generalized hamming weights

The Feng-Rao bound gives good estimates of the minimum distance of a large class of codes. In this work we are concerned with the problem of how to extend the Feng-Rao bound so that it deals with all the generalized Hamming weights. The problem was solved by Heijnen and Pellikaan in [7] for a large family of codes that includes the duals of one-point geometric Goppa codes and the q-ary Reed-Muller codes, but not the Feng-Rao improved such ones. We show that Heijnen and Pellikaan’s results holds for the more general class of codes for which the traditional Feng-Rao bound can be applied. We also establish the connection to the Shibuya-Sakaniwa bound for generalized Hamming weights ([15], [16], [17], [18], [19] and [20]). More precisely we show that the Shibuya-Sakaniwa bound is a consequence of the extended Feng-Rao bound. In particular the extended Feng-Rao bound gives always at least as good estimates as does the Shibuya-Sakaniwa bound.

Error-correcting capabilities of concatenated codes with MDS outer codes on memoryless channels with maximum- likelihood decoding

Error-correcting capabilities of concatenated codes with maximum distance separable (MDS) outer codes and time-varying inner codes, used on memoryless discrete channels with maximum-likelihood decoding, are investigated. It is proved that, asymptotically, the Gallager random coding theorem can be obtained for all rates by such codes. Further, the expurgated coding theorem, as well, is proved to be valid for all rates on regular channels. The latter result implies that the Gilbert-Varshamov bound for block codes over any finite field can be obtained asymptotically for all rates by linear concatenated codes.

On spatial power gradients

The variation of the instantaneous power versus distance for a narrowband channel is an important parameter in modern digital systems, relevant for variations during a burst and for power control algorithms. This paper gives the statistical distribution for the power gradient, both in decibels and in natural units for a Rayleigh fading channel. The former has been known for some time to be Students t distribution, and the latter has a Laplacian distribution, a new result. Both results are proven here. They are in variance with an approximation given in a previous publication.

Concatenated codes with fixed inner code, and the outer code randomly selected

A lower bound for the above given coding scheme, where the inner and outer codes are block codes, is derived. The bound, which depends on the outer code rate, and the weight distribution of the inner code, is compared to the Gilbert-Varshamov bound for block codes.<<ETX>>

A stochastic model in mobile communications

We propose a stochastic model for the variations in the transfer function for the mobile communication environment based on the complex Gaussian distribution. The model is a slight generalization of the classical and allows the characteristics of the scenario to be frequency dependent. Under the assumptions of this model we show that the group delay and instantaneous Doppler shift both follow a Students t distribution with two degrees of freedom.