Alexey Kreshchuk

Generalized error-locating codes and minimization of redundancy for specified input and output error probabilities

Generalized error-locating codes are discussed. An algorithm for calculation of the upper bound of the probability of erroneous decoding for known code parameters and the input error probability is given. Based on this algorithm, an algorithm for selection of the code parameters for a specified design and input and output error probabilities is constructed. The lower bound of the probability of erroneous decoding is given. Examples of the dependence of the probability of erroneous decoding on the input error probability are given and the behavior of the obtained curves is explained.

Generalized concatenated system with embedded space-time codes for MIMO systems

Multiple-input multiple-output systems are communication systems employing multiple transmitting and receiving antennas. In the present study, a new generalized concatenated signal-code construction is proposed. Its inner codes are embedded Golden codes, and its outer codes are products of Reed-Solomon codes. New algorithms for decoding inner codes, outer codes, and the generalized signal-code construction itself are proposed. The decoder for space-time Golden codes makes it possible to obtain a measure of reliability for certain symbols without an increase in the number of arithmetic operations. The decoder for outer product codes removes the “floor” on the error-probability curve. In addition, the lower bounds of decoding-error probability for the product-code iterative decoders have been obtained. The error-correcting capacity of the new decoder for the generalized concatenated construction is higher than that of the currently known decoders. A computer simulation has shown the efficiency of the proposed construction and decoding algorithms.

Statistical demodulators for frequency shift keying with fast frequency hopping

This work is devoted to the problems of information transmission with frequency shift keying and fast frequency hopping in special channels where the signal/noise ratio is low, and a high energy interfering signal is present. We propose a demodulation algorithm that is significantly more stable to the influence of a powerful interfering signal as compared to other known algorithms. Under these conditions, we show a statistical criterion that lets one significantly reduce error probability on the demodulator’s output. For the chosen criterion we prove several lemmas that let us speed up the demodulation algorithm. Computer modeling results show that the proposed demodulation algorithm has better correcting ability under a powerful interfering signal than previously known ones.

On the code distance of a woven block code construction

In this paper we propose a woven block code construction based on two convolutional outer codes and a single inner code. We proved lower and upper bounds on this constructions code distance. The lower bound is shown to be higher than the product of the free distances of inner and outer constituent codes. Since this construction uses well-developed convolutional constituent codes, we believe that it would be competitive to turbo codes in the future mobile communication systems.

Codes for MIMO transmission based on orthogonal sequences

We consider MIMO communication systems with Rayleigh fading. We propose a new coded modulation based on orthogonal sequences and state a new decodability condition. We introduce concepts and constructions of permutation free (PF) and permutation and repetition free (PRF) codes. We also propose a construction of PRF codes with sign manipulation, whose code rate can exceed 1. For better analysis and construction of these codes we introduce a one-to-one mapping that transforms signal matrices to vectors over a finite field. We propose construction algorithms for PF and PRF codes. We build PF and PRF codes with large cardinality, which in several case achieve the maximum cardinality. Simulation of the constructed codes and estimation of their performance was done in Simulink environment. Results show high error-correcting capability, which often reaches that of STBC codes with full transmit diversity.

On the Performance of Block Woven Codes Constructions with Row-Wise Permutations.

In this paper we propose a woven block code construction based on two convolutional codes. We also propose a soft-input decoder that allows this construction to have better error correction performance than the turbo codes with a conventional decoder. Computer simulation has showed a 0.1 dB energy gain relative to the LTE turbo code. Asymptotically the proposed code has distance greater than the product of free distances of component codes.

Upper bounds on the smallest size of a complete cap in PG(3,q) and PG(4,q)

Abstract In this work we summarize some recent results to be included in a forthcoming paper [Bartoli, D., A. A. Davydov, A. A. Kreshchuk, S. Marcugini and F. Pambianco, Small complete caps in PG ( 3 , q ) and PG ( 4 , q ) , preprint]. We present and analyze computational results concerning small complete caps in the projective spaces PG ( N , q ) of dimension N = 3 and N = 4 over the finite field of order q. The results have been obtained using randomized greedy algorithms and the algorithm with fixed order of points (FOP). The new complete caps are the smallest known. Based on them, we obtained new upper bounds on the minimum size t 2 ( N , q ) of a complete cap in P G ( N , q ) , N = 3 , 4 . Our investigations and results allow to conjecture that these bounds hold for all q.

Better goodness-of-fit statistics for coded FSK decoding

Abstract In previous papers we have considered fast-frequency hopping frequency shift keying. We have proposed a decoder with low error rate in channels with low signal to interference ratio. This decoder uses the Kolmogorov-Smirnov criterion statistics to differentiate transmitted codeword from others. In this paper we consider different goodness-of-fit criterion to improve the decoder error rate. We have discovered that the decoder based on the Barnett-Eison criterion have lower error rates in wideband interference scenario, while the one based on the Anderson criterion is better in case of narrowband interference.

On applying one-sample goodness-of-fit statistics to coded FSK decoding

In the previous works we have considered decoding coded FSK modulation (similar to Kautz-Singleton codes) transmitted in a channel with strong interference by using a two-sample goodness-of-fit statistics. In this work we consider the applicability of different one-sample goodness-of-fit statistics for the decoding. Using a computer simulation we show that using these statistics may yield lower error rates relative to the known decoders. The most notable of them are Anderson Darling statistic that has the lowest error rates for narrow-band interference and Pearsons x2 and Kuiper statistics that are more resilient to wide-band interference. We can conclude that one-sample goodness-of-fit statistics can be used for Kautz-Singleton codes decoding with relatively low error rates in case of strong interference in the channel.

Generalized concatenated MIMO system with GMD decoding

In this paper we propose new coded modulation for multiple-input and multiple-output (MIMO) communication systems. This coded modulation is a generalized concatenated code. Its inner code is embedded Golden code which we introduce in this paper with a decoding algorithm. Its outer code is a product code with component Reed-Solomon code. We propose iterative decoding algorithm for this product code. We also propose an generalized minimum distance decoder for generalized concatenated code. The performance of the proposed system is estimated with a computer simulation.