Fedor Ivanov

Low-density parity-check codes based on the independent subgroups

Two criteria of cyclic subgroups independence are proved. The ensemble of regular binary LDPC codes which are based on independent subgroups, is built. The condition of absence of the cycles of the length 4 is proved for the resulting code construction. The results of the received code constructions are presented for the iterative algorithm Sum-Product when the codeword is transmitted over channel with additive Gaussian white noise (AGWN).

Low-density parity-check codes based on steiner systems and permutation matrices

An algorithm for generating parity-check matrices of regular low-density paritycheck codes based on permutation matrices and Steiner triple systems S(v, 3, 2), v = 2m − 1, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm applied in the case of transmission over a binary channel with additive Gaussian white noise and BPSK modulation are presented.

Low-density parity-check codes based on Galois fields

Methods for constructing a mapping of the elements of a multiplicative group of a Galois field onto a symmetric group of permutation matrices are proposed. A technique minimizing the order of the symmetric group is suggested. The results are used for constructing an ensemble of low-density parity-check codes. The obtained code constructions are tested on an iterative belief propagation (sum-product) decoding algorithm on transmission of a code word through a binary channel with an additive Gaussian white noise.

Comparison of Various Constructions of Binary LDPC Codes Based on Permutation Matrices

Ensembles of low-density parity check codes based on permutation matrices are considered. Algorithms for generation of check matrices of such codes are proposed. The results of simulation of the obtained code constructions for an iterative belief propagation (sum-product) decoding algorithm applied in the case of transmission of a code word via a binary channel with an additive Gaussian white noise are presented.

A special class of quasi-cyclic low-density parity-check codes based on repetition codes and permutation matrices

We propose a new ensemble of binary low-density parity-check codes with paritycheck matrices based on repetition codes and permutation matrices. The proposed class of codes is a subensemble of quasi-cyclic codes. For the constructed ensemble, we obtain minimum distance estimates. We present simulation results for the proposed code constructions under the (Sum-Product) iterative decoding algorithm for transmission over an additive white Gaussian noise channel using binary phase-shift keying.

Vectorizing computations at decoding of nonbinary codes with small density of checks

A modification of the decoding q-ary Sum Product Algorithm (q-SPA) was proposed for the nonbinary codes with small check density based on the permutation matrices. The algorithm described has a vector realization and operates over the vectors defined on the field GF(q), rather than over individual symbols. Under certain code parameters, this approach enables significant speedup of modeling.

On iterative LDPC-based joint decoding scheme for binary input Gaussian multiple access channel

Non-orthogonal multiple access schemes are of great interest for next generation wireless systems, as such schemes allow to reduce the total number of resources (frequencies or time slots) in comparison to orthogonal transmission (TDMA, FDMA, CDMA). In this paper we consider an iterative LDPC-based joint decoding scheme suggested in [1]. We investigate the most difficult and important problem where all the users have the same power constraint and the same rate. For the case of 2 users we use a known scheme and analyze it by means of simulations. We found the optimal relation between the number of inner and outer iterations. We further extend the scheme for the case of any number of users and investigated the cases of 3 and 4 users by means of simulations. Finally, we showed, that considered non-orthogonal transmission scheme is more efficient (for 2 and 3 users), than orthogonal transmission.

Low-Density Parity-Check codes based on Partial Unit Memory codes

In this paper we describe ensemble of Low-Density Parity-Check (LDPC) block codes based on Partial Unit Memory (P)UM codes. We study a decoding performance of received ensemble in the case of different parameters of constituent LDPC codes. The results of simulation of obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm, applied in the case of transmission of a code word via a binary channel with an additive Gaussian white noise and BPSK modulation, are presented.