# Irina E. Bocharova's research while affiliated with University of Tartu and other places

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## Publications (82)

This paper studies specific properties of nonbinary low-density parity-check (NB LDPC) codes when used in coded modulation systems. The paper is focused on the practically important NB LDPC codes over the Galois extension fields GF
$(2^{m})$
with
$m\le 6$
used with QAM signaling. Performance of NB LDPC coded transmission strongly depends on the...

We propose a novel approach to optimization of irregular nonbinary (NB) quasi-cyclic (QC)-LDPC codes over small alphabets. In this approach, first, the base parity-check matrices are constructed by a simulated annealing method, and then these matrices are labeled by the field elements while maximizing the so- called generalized girth of the Tanner...

The goal of the paper is to study specific properties of nonbinary low-density parity-check (NB LDPC) codes when used in coded modulation systems. The paper is focused on the practically important NB LDPC codes over extensions of the Galois field GF$(2^m)$ with $m \le 6$ used with QAM signaling. Performance of NB QC LDPC coded transmission strongly...

We propose an approach for optimizing nonbinary (NB) quasi-cyclic (QC) LDPC codes. This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the so-called generalized girth of the NB LDPC code Tanner graph. Tightened random coding bounds based on the average...

In Cooperative Intelligent Transportation Systems (C-ITSs), vehicles need to wirelessly connect with Roadside units (RSUs) over limited durations when such point-to-point connections are possible. One example of such communications is the downloading of maps to the C-ITS vehicles. Another example occurs in the testing of C-ITS vehicles, where the t...

To enable testing and performance evaluation of new connected and autonomous driving functions, it is important to characterize packet losses caused by degradation in vehicular (V2X) communication channels. In this paper we suggest an approach to constructing packet loss models based on the so-called Pseudo-Markov chains (PMC). The PMC based model...

Stopping sets play a crucial role in failure events of iterative decoders over a binary erasure channel (BEC). The $l$-th stopping redundancy is the minimum number of rows in the parity-check matrix of a code, which contains no stopping sets of size up to $\ell$. In this work, a notion of coverable stopping sets is defined. In order to achieve maxi...

The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is computed by using a recurrent procedure and compared to the empirically found average spectrum for the same ensem...

Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel are studied. Both random and structured LDPC codes are considered. In particular, the BP decoding is applied...

Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel are studied. Both random and structured LDPC codes are considered. In particular, the BP decoding is applied...

A new method for low-complexity near-maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over the additive white Gaussian noise channel is presented. The proposed method termed belief-propagation--list erasure decoding (BP-LED) is based on erasing carefully chosen unreliable bits performed in case of BP decoding failure. A str...

A novel method of low-complexity near-maximum-likelihood (ML) decoding of quasi-cyclic (QC) low-density parity-check (LDPC) codes over the binary erasure channel is presented. The idea is similar to wrap-around decoding of tail-biting convolutional codes. ML decoding is applied to a relatively short window which is cyclically shifted along the rece...

A unified approach to search for and optimize codes determined by their sparse parity-check matrices is presented. Replacing the nonzero elements of a binary parity-check matrix (the base or parent matrix) either by circulants or by companion matrices of elements from a finite field GF $(2^{m})$ , we obtain quasi-cyclic low-density parity-check (LD...

A source-channel coding scheme in which source messages are assigned to two classes and encoded using a channel code that depends on the class index is studied. A low-complexity implementation with two quasi-cyclic LDPC codes with belief-propagation decoding achieves a better frame error rate than optimized separate coding. The coding gain obtained...

We study a source-channel coding scheme in which source messages are assigned
to different classes and encoded using a channel code that depends on the class
index. The performance of this scheme is studied by means of random-coding
error exponents and validated by simulation of a low-complexity implementation
using existing source and channel code...

In this paper we investigate the highly bandwidth-efficient Faster-than-Nyquist (FTN) signaling scheme under high order modulations. The FTN system is an emerging technology which has drawn attention in the contemporary spectrum-saving communication environment. Since FTN traditionally achieves high bandwidth efficiency through increased baud-rate,...

A unified approach to construct and optimize codes determined by their sparse parity-check matrices is presented. Parity-check matrices of quasi-cyclic (QC) LDPC block codes are obtained by replacing the nonzero elements of a base (seed) matrix by circulants. Replacing the nonzero elements either by companion matrices of elements from a finite fiel...

We study a source-channel coding scheme in which source messages are assigned to classes and encoded using a channel code that depends on the class index. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint s...

Outstanding asymptotical performance demonstrated by low-density parity-check (LDPC) convolutional codes (CC) makes them strong competitors with respect to quasi-cyclic (QC) LDPC block codes (BC) currently used in a variety of communication standards. However, typically communication standards, for example, DVB-S2 or WIMax standards impose rather s...

Techniques for searching for good quasi-cyclic (QC) LDPC block codes of short and moderate lengths which are suitable for practical purposes are studied. To facilitate implementations only codes whose parity-check matrices having bidiagonal structure of their submatrices and consequently having low encoding complexity are considered. The problem of...

Relations between Generalized LDPC codes, nonbinary LDPC codes, and woven graph codes are considered. Focus is on rather short codes suitable, for example, for coding control signaling information in mobile communications. In particular, codes of lengths less than 200 bits are studied. Low-complexity near maximum-likelihood (ML) decoding for these...

Irregular QC LDPC codes with parity-check matrices having different degree distributions are studied. A new algorithm for finding regular and irregular QC LDPC codes with a good girth profile as well as a good sliding-window girth is presented. As examples, simulation results for QC LDPC codes with good girth profile, rate R=4/5, and lengths about...

The girth profile is introduced and search algorithms for regular and irregular quasi-cyclic LDPC block codes with both good girth profile and good degree distribution are presented. New QC LDPC block codes of various code rates are obtained and their bit error rate performance is compared with that of the corresponding LDPC block codes defined in...

A recursion for sequences of spectra of truncated as well as tailbitten convolutional codes and their duals is derived. The order of this recursion is shown to be less than or equal to the rank of the weight adjacency matrix (WAM) for the minimal encoder of the convolutional code. It is sufficient to know finitely many spectra of these terminated c...

In 1995, Best et al. published a formula for the exact bit error probability
for Viterbi decoding of the rate R=1/2, memory m=1 (2-state) convolutional
encoder with generator matrix G(D)=(1 1+D) when used to communicate over the
binary symmetric channel. Their formula was later extended to the rate R=1/2,
memory m=2 (4-state) convolutional encoder...

The relation between the parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and the biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Algorithms for searching iteratively for LDPC block codes with large girth are presented and constructions based on Steiner Triple Systems and sh...

A new method using Hamming codes to construct base matrices of (J,K)-regular LDPC convolutional codes with large free distance is presented. By proper labeling the corresponding base matrices and tailbiting these parent convolutional codes to given lengths, a large set of quasi-cyclic (QC) (J,K)-regular LDPC block codes with large minimum distance...

The relation between parity-check matrices of quasi-cyclic (QC) low-density
parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports
searching for powerful LDPC block codes. Using the principle of tailbiting,
compact representations of bipartite graphs based on convolutional codes can be
found.
Bounds on the girth and the min...

Forty years ago, Viterbi published upper bounds on both the first error event (burst error) and bit error probabilities for Viterbi decoding of convolutional codes. These bounds were derived using a signal flow chart technique for convolutional encoders. In 1995, Best et al. published a formula for the exact bit error probability for Viterbi decodi...

Constructions of woven graph codes based on constituent convolutional codes are studied, and examples of woven convolutional
graph codes are presented. Existence of codes satisfying the Costello lower bound on the free distance within a random ensemble
of woven graph codes based on s-partite, s-uniform hypergraphs is shown, where s depends only on...

The relation between low-density parity-check (LDPC) codes and hypergraphs supports searching for powerful LDPC codes based on hypergraphs. On the other hand, coding theory methods can be used in searching for hypergraphs with large girth. Moreover, compact representations of hypergraphs based on convolutional codes can be found. Algorithms for ite...

A rate R=5/20 hypergraph-based woven convolutional code with overall constraint length 67 and constituent convolutional codes is presented. It is based on a 3-partite, 3-uniform, 4-regular hypergraph and contains rate R<sup>c</sup>=3/4 constituent convolutional codes with overall constraint length 5. Although the code construction is based on low-c...

Convolutional codes are defined to be equivalent if their code symbols differ only in how they are ordered and two generator matrices are defined to be weakly equivalent (WE) if they encode equivalent convolutional codes. It is shown that tailbiting convolutional codes encoded by WE minimal-basic generator matrices have the same spectra. Shearer an...

Constructions of woven graph codes based on constituent block and convolutional codes are studied. It is shown that within the random ensembles of such codes based on s-partite, s-uniform hypergraphs, where s depends only on the code rate, there exist codes satisfying the Gilbert-Varshamov (GV) and the Costello lower bound on the minimum distance a...

We consider regular block and convolutional LDPC codes determined by paritycheck matrices with rows of a fixed weight and
columns of weight 2. Such codes can be described by graphs, and the minimum distance of a code coincides with the girth of
the corresponding graph. We consider a description of such codes in the form of tail-biting convolutional...

We search for good regular quasi-cyclic (QC) LDPC codes with J = 2 ones in each column. In order to simplify the search, QC LDPC codes are represented in the form of tail-biting (TB) convolutional codes. A modified BEAST algorithm is used for finding the free distance (minimum distance) and the girth of both parent convolutional and block LDPC code...

Rate R = (c-1)/c convolutional codes of constraint length Â¿ can be represented by conventional syndrome trellises with a state complexity of s = Â¿ or by binary syndrome trellises with a state complexity of s = Â¿ or s = Â¿ + 1, which corresponds to at most 2<sup>s</sup> states at each trellis level. It is shown that if the parity-check polynomial...

Constructions of woven graph codes based on constituent block and convolutional codes are studied. It is shown that within the random ensemble of such codes based on s-partite, s-uniform hypergraphs, where s depends only on the code rate, there exist codes satisfying the Varshamov-Gilbert (VG) and the Costello lower bound on the minimum distance an...

A bidirectional efficient algorithm for searching code trees (BEAST) is proposed for efficient soft-output decoding of block codes and concatenated block codes. BEAST operates on trees corresponding to the minimal trellis of a block code and finds a list of the most probable codewords. The complexity of the BEAST search is significantly lower than...

List decoding of binary block codes for the additive white Gaussian noise (AWGN) channel is considered. The output of a list decoder is a list of the most likely codewords, that is, the signal points closest to the received signal in the Euclidean-metric sense. A decoding error occurs when the transmitted codeword is not on this list. It is shown t...

This paper reviews soft-input soft-output (SISO) algorithms that have been recently proposed as reduced-complexity alternatives to maximum a posteriori (MAP) trellis-based decoding or equalization. The M*-BCJR, LISS, and BEAST algorithms are chosen as representatives of reduced-state trellis- and tree-search procedures. The former two algorithms ha...

A construction of woven graph codes based on constituent convolutional codes is studied. It is shown that within the random ensemble of such codes there exist asymptotically good codes with short fixed constituent codes. An example of a rate R = 1/3 woven graph code with free distance equal to 32 based on rate R c = 2/3 constituent convolutional co...

An extended table of Shuurman's bounds on the state complexity of short binary linear codes is presented. Some new lower and upper bounds are obtained. Most of the newly found codes are based on the so-called double zero-tail termination (DZT) construction

The performance and convergence behavior of the iterative schemes for decoding two-dimensional product codes are investigated. The decoding trajectories of the extrinsic and the a posteriori information are used as a main tool for predicting and explaining the behavior of the iterative decoding process. The component-wise optimal BCJR decoder is co...

This paper presents a low-complexity iterative algorithm for decoding concatenated block codes, in particular, product codes. Component decoders in the iterative scheme are based on BEASTÂ¿Bidirectional Efficient Algorithm for Searching code Trees. BEAST finds a list of the most probable codewords and uses them to compute approximate a posteriori s...

We consider the problem of minimizing the number of multiplications in computing f(x)=x
n
, where n is an integer and x is an element of any ring. We present new methods which reduce the average number of multiplications comparing with well-known methods, such as the binary method and the q-ary method. We do not compare our approach with algorithm...

The BEAST-APP decoding algorithm is a low-complexity bidirectional algorithm that searches code trees to find the list of the most likely codewords, which are used to compute approximate a posteriori probabilities (APPs) of the transmitted symbols. It can be applied to APP-decoding of any linear block code, as well as in iterative structures for de...

BEAST is a bidirectional efficient algorithm for searching trees that performs soft-decision maximum-likelihood (ML) decoding of block codes. The decoding complexity of BEAST is significantly reduced compared to the Viterbi algorithm. An analysis of the asymptotic BEAST decoding complexity verifies BEAST's high efficiency compared to other algorith...

A new class of block codes with low state complexity of their conventional trellis representations called double zero-tail terminated convolutional codes (DZT codes) is introduced. It is shown that there exist DZT-codes meeting the Varshamov-Gilbert bound on the minimum distance and having asymptotically optimal state complexity. Two ways of constr...

When searching for convolutional codes and tailbiting codes of high complexity it is of vital importance to use fast algorithms for computing their weight spectra, which corresponds to finding low-weight paths in their code trellises. This can be efficiently done by a combined search in both forward and backward code trees. A bidirectional efficien...

BEAST is a Bidirectional Efficient Algorithm for Searching code Trees. In this paper, it is used for decoding block codes over a binary-input memoryless channel. If no constraints are imposed on the decoding complexity (in terms of the number of visited nodes during the search), BEAST performs maximum-likelihood (ML) decoding. At the cost of a negl...

Good approximations of code-symbol a-posteriori probabilities (APPs) are obtained using a list of the most likely codewords, instead of the whole code-book. This list is found by bidirectional efficient algorithm for searching code trees (BEAST), whose complexity is shown to be lower than of the known trellis-based algorithms

The slope of the active distances is an important parameter when investigating the error-correcting capability of convolutional codes and the distance behavior of concatenated convolutional codes. The slope of the active distances is equal to the minimum average weight cycle in the state-transition diagram of the encoder. A general upper bound on t...

A bidirectional algorithm for computing spectral coefficients of convolutional and tailbiting codes is presented and used to obtain new codes.

Upper bounds on the slope of the active distances for convolutional codes are given. Convolutional codes with large slopes are used to obtain tables of new tailbiting block codes.

Tailbiting trellis representations of linear block codes with an
arbitrary sectionalization of the time axis are studied. The notations
of regular and irregular tailbiting codes are introduced and their
maximal state complexities are lower-bounded. The asymptotic behavior of
the derived bound is investigated. Furthermore, for regular tailbiting
cod...

Tailbiting trellis representations of linear block codes with an
arbitrary sectionalization of the time axis are studied. A new lower
bound on the maximal state complexity of an arbitrary tailbiting code is
derived. The asymptotic behavior of the derived bound is investigated.
Some new tailbiting representations for linear block codes of rates
R=1/...

We present rational rate k/n punctured convolutional codes (n up
to 8, k=1, ···, n-1, and constraint length ν up
to 8) with good performance. Many of these codes improve the free
distance and (or) weight spectra over previously reported codes with the
same parameters. The tabulated codes are found by an exhaustive (or a
random) search

We consider a problem of calculating covering capabilities for convolutional codes. An upper bound on covering radius for convolutional code is obtained by random coding arguments. The estimates on covering radius for some codes with small constraint length are presented.

We consider the problem of efficient codebook search for the code excited linear predictive (CELP) speech coders. To dimmish the search complexity a trellis codebook is proposed and decoding algorithms based on the Viterbi algorithm are investigated. Numerical results of the computer simulation are presented.

The problem of reducing the number of multiplications in infinite response filtering is considered. We show how this operation may be decomposed on finite response filtrations and so-named halfconvolutions. Examples of the efficient procedures for filters of low order are presented.

## Citations

... Moreover, low-complexity encoding algorithms have also been well recognized [14]. Recent research in the field also involves nonbinary coding algorithms, as well as code design and implementation [28][29][30]. ...

... However, in BG, a more complex version of TTL is used. In this version, the decoder creates two lists of bit nodes (called Black and Gray lists) to keep track of those bit flips that are regarded as "uncertain" [54]. The first list (i.e., Black) maintains the positions of those bit nodes that were just flipped. ...

... Due to the growing percentage of people using these technologies, methods are needed to increase the transmission rate without reducing the quality [4] [5]. One of these methods is the Reed-Solomon (RS) and BCH codes which are used to correct errors in many systems such as Vehicular Networks, storage devices (CD, DVD, etc.) and digital video broadcasting (DVB) [6][7] [8]. An RS code word is a packet of symbols which are commonly bytes (8bit symbols), denotes as RS (n, k) where n is the number of the symbols in the encoded message and k is the number of the symbols in the original message as shown in Fig.1. ...

... A technique called adaptive auxiliary variable node (AAVN) was proposed in [BJK19]. It adds columns and rows to the parity check matrix in order to remove some cycles of length 4 in the Tanner graph as small cycles are known to be detrimental to decoders. ...

... However, in this paper, we consider both memoryless BEC and BEC with memory (M-BEC). One example of M-BEC model is obtained from the wireless fading channel model by applying discrete model constructing technique in [19,20]. ...

... However, in this paper, we consider both memoryless BEC and BEC with memory (M-BEC). One example of M-BEC model is obtained from the wireless fading channel model by applying discrete model constructing technique in [19,20]. ...

... Two low-complexity sliding-window (SW)-decoding procedures are studied. The first one is based on ML-decoding applied to the ZT convolutional code inside the window and the second implies conventional BP decoding and BP decoding with using redundant parity-check (RPC) matrix of the same code [26,27]. As explained below, RPC matrix contains linear dependent rows which destroy stopping sets of the code and improve erasure correcting capability compared to BP decoding while preserving low decoding complexity. ...

... In particular, for comparison of the performance over the BEC, we use the improved upper bound (3) computed for the precise ensemble average spectrum coefficients for both random linear code and (3, 6)-regular random binary LDPC code. As a lower bound, we consider the tighten sphere-packing bound in [6]. For comparison of the performance over the AWGN channel, we show the tangential-sphere upper bound [25] computed with the precise ensemble average spectrum coefficients for the same two ensembles and the Shannon lower bound [30]. ...

... Finite length upper bounds on error probability of ML decoding over the AWGN channel obtained by using precise average weight enumerators for both binary random regular LDPC codes and for random regular NB LDPC codes over GF(2 m ) along with the asymptotic ML decoding thresholds were derived in [17]. In this paper by using technique in [18] for computing precise average spectra for ensembles of LDPC codes, we derive a tighter bound on error probability of the ML decoding for the ensemble of 'almost regular" NB LDPC codes over GF (2 m ). ...

... In [27], asymptotic average Hamming weight spectra for ensembles of regular NB LDPC codes over GF(2 m ) were obtained. In [28], we presented a low-complexity recurrent procedure for computing exact Hamming weight spectra of both binary and NB random ensembles of regular LDPC codes. ...