Kamil Sh. Zigangirov

Iterative Decoding Threshold Analysis for LDPC Convolutional Codes

An iterative decoding threshold analysis for terminated regular LDPC convolutional (LDPCC) codes is presented. Using density evolution techniques, the convergence behavior of an iterative belief propagation decoder is analyzed for the binary erasure channel and the AWGN channel with binary inputs. It is shown that for a terminated LDPCC code ensemble, the thresholds are better than for corresponding regular and irregular LDPC block codes.

Approaching capacity with asymptotically regular LDPC codes

We present a family of protograph based LDPC codes that can be derived from permutation matrix based regular (J,K) LDPC convolutional codes by termination. In the terminated protograph, all variable nodes still have degree J but some check nodes at the start and end of the protograph have degrees smaller than K. Since the fraction of these stronger nodes vanishes as the termination length L increases, we call the codes asymptotically regular. The density evolution thresholds of these protographs are better than those of regular (J, K) block codes. Interestingly, this threshold improvement gets stronger with increasing node degrees (at a fixed rate) and it does not decay as L increases. Terminated convolutional protographs can also be derived from standard irregular protographs and may exhibit a significant threshold improvement.

On the Theory of Low-Density Convolutional Codes

We introduce and analyze a new statistical ensemble of low-density parity-check convolutional (LDC) codes. The result of the analysis are bounds, such as a lower bound for the free distance and upper bounds for the burst error probability of the LDC codes.

Decoders for low-density parity-check convolutional codes with large memory

Low-density parity-check convolutional codes offer the same good error-correcting performance as low-density parity-check block codes while having the ability to encode and decode arbitrary lengths of data. This makes these codes well suited to certain applications, such as forward error control on packet switching networks. In this paper we propose a decoder architecture for low-density parity-check convolutional codes with very large memories. These codes have very good error correcting properties and as such may be applicable in wireless sensor networks and space communication systems. We discuss a realization of this architecture for a (2048,3,6) code implemented on a field-programmable gate-array

Construction of Irregular LDPC Convolutional Codes with Fast Encoding

We propose a novel code design technique for irregular LDPC convolutional codes. The constructed codes can be encoded continuously in real time with the help of a shift-register based encoder. For moderate values of the syndrome former memory, simulation results show that the constructed codes outperform LDPC block codes with comparable hardware (processor) complexity.

Braided convolutional codes

We present a new class of iteratively decodable turbo-like codes, called braided convolutional codes. Constructions and encoding procedures for tightly and sparsely braided codes are introduced. Sparsely braided codes exhibit good convergence behavior with iterative decoding, and a statistical analysis using Markov permutors shows that the free distance of these codes grows linearly with constraint length.

Minimum distance bounds for multiple-serially concatenated code ensembles

It has recently been shown that the minimum distance of the ensemble of repeat multiple accumulate codes grows linearly with block length. In this paper, we present a method to obtain the distance growth rate coefficient of multiple-serially concatenated code ensembles and determine the growth rate coefficient of the rate 1/2 double-serially concatenated code consisting of an outer memory one convolutional code followed by two accumulators. We compare both the growth rate of the minimum distance, as well as the convergence behavior, of this code with rate 1/2 repeat multiple accumulate codes, and we show that repeat multiple accumulate codes have better minimum distance growth but worse performance in terms of convergence.

Analysis of Global-List Decoding for Convolutional Codes

Department of Information Theory University of Lund Box 118 S- 221 00 Lund - Sweden n n n nIn this paper we consider the global-list decoding algorithm for convolutional codes. We introduce the notion of the L-list minimum distance and prove lower and upper bounds for if. Furthermore, we derive lower and upper bounds for the decoding error probability of the global- list decoding.

On the free distance of LDPC convolutional codes

A lower bound on the free distance of LDPC convolutional codes defined by syndrome former matrices comprised of MtimesM permutation matrices is derived. We show that asymptotically, i.e., as Mrarrinfin, for almost all codes in the ensemble the free distance grows linearly with constraint length

Encoders and Decoders for Braided Block Codes

We consider construction and realization aspects of encoders and decoders for braided block codes (BBCs), which are a powerful class of iteratively decodable codes. An efficient encoder is proposed as well as a pipeline decoder realization. Also, upper and lower bounds on the free distance of BBCs are derived