Nikolai L. Manev

An improvement of the Griesmer bound for some small minimum distances

Abstract In this paper we give some lower and upper bounds for the smallest length n ( k , d ) of a binary linear code with dimension k and minimum distance d . The lower bounds improve the known ones for small d . In the last section we summarize what we know about n (8, d ).

New bounds on binary linear codes of dimension eight (Corresp.)

Let n(k,d) be the smallest integer n such that a binary linear code of length n , dimension k , and minimum distance at least d exists. New results are given that improve the best previously known bounds on n(8,d) .

On the non-minimal codewords in binary Reed--Muller codes

First, we compute the number of non-minimal codewords of weight 2dmin in the binary Reed-Muller code RM(r,m). Second, we prove that all codewords of weight greater than 2m - 2m-r+1 in binary RM(r,m), are non-minimal.

Derivation on bit error probability of coded QAM using integer codes

Coded modulation refers to the process of combined and jointly optimized channel coding and modulation scheme. In this paper, block coded modulation using integer codes and its performance is evaluated by deriving a formula of its bit error probability for AWGN channel. The probability of correct detection of the received signal is a square of the corresponding probability. The detector correctly demodulates the received signal with an average probability in uncoded and coded case respectively.

Double error correctable integer code and its application to QAM

A new construction of double error correctable integer codes and their application to QAM scheme are presented. Soft decoding algorithm for multiple error correctable integer code which are suited to any modulation scheme (QAM, PSK, ASK) will be introduced. Comparison of bit error rate (BER) versus signal-to-noise ratio (SNR) between soft and hard decoding using integer coded modulation (ICM) shows us that we can obtain approximately 2 dB coding gain.

New Bounds for Probability of Error of Coded and Uncoded TQAM in AWGN Channel

We investigate the performance of coded modulation scheme based on the application of integer codes to triangular quadrature amplitude modulation (TQAM). An upper and a lower bounds for symbol error probability (SER) in the case of AWGN channel are derived. These bounds are so closed that it makes the calculation of the exact value of SER unnecessary in practice.

Monte Carlo Methods Using New Class of Congruential Generators

In this paper we propose a new class of congruential pseudo random number generator based on sequences generating permutations. These sequences have been developed for other applications but our analysis and experiments show that they are appropriate for approximation of multiple integrals and integral equations.

On the Probability of Error for Triangular Quadrature Amplitude Modulation

Abstract We compute the exact value of error probability per symbol (SER) for triangular quadrature amplitude modulation (TQAM) scheme in the case of AWGN channel. The results show that the exact value of SER follows the behavior of the known upper bound [Kostadinov, H., L. Kraleva and N. L. Manev, New Bounds for Probability of Error of Coded and Uncoded TQAM in AWGN Channel, Advanced Computing in Industrial Mathematics, 681 (2017)]. Hence a simple modification of the upper bound can be used in practice for evaluating the SER.

Numerical integration using sequences generating permutations

In this paper we propose a new class of pseudo random number generators based on a special linear recursions modulo m. These generators produce sequences which are permutations of the elements of a ℤm. These sequences have been developed for other applications but the analysis of their statistical properties and the experiments described in this paper show that they are appropriate for multiple integration. Here we present some results from numerical tests comparing the performance of the two proposed generators with Mersenne Twister.

On coded modulation based on finite rings of integers

In this paper, we investigate the problem how to use codes over /spl Zopf//sub A/ to correct any single error which belongs to the set {/spl plusmn/e/sub 1/,/spl plusmn/e/sub 2/,...,/spl plusmn/e/sub s/}, where e/sub i/s are different elements in /spl Zopf//sub A/. We present some classes of such codes and describe how they can be applied to M-QAM.