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High-rate low-density parity-check (LDPC) codes are the focus of intense research in magnetic recording because, when decoded by the iterative sum-product algorithm, they show decoding performance close to the Shannon capacity. However, cycles, especially short cycles, are harmful to LDPC codes. The paper describes the partition-and-shift LDPC (PS-LDPC) codes, a new class of regular, structured LDPC codes that can be designed with large girth and arbitrary large minimum distance. Large girth leads to more efficient iterative decoding and codes with better error-floor properties than random LDPC codes. PS-LDPC codes can be designed for any desired column weight and with flexible code rates. The paper details the girth and distance properties of the codes and their systematic construction and presents analytical and simulation performance results that show that, in the high signal-to-noise ratio region, PS-LDPC codes out- perform random codes, alleviating the error floor phenomenon. [ABSTRACT FROM AUTHOR]

In this paper, we employ selective bit mapping to improve the performance of the LDPC coded QAM scheme for terrestrial DTV broadcasting system. The threshold of message-passing decoding can be considerably lowered by selectively mapping the binary components of LDPC codeword to the positions in the m-tuples to be mapped into 2^mQAM symbols. In our approach, the mapping pattern is described by bit-mapping polynomials, based on which density evolution can be applied. The optimization algorithm is developed with two implementation concerns, using the Chinese DTMB standard as an example. Numerical results illustrate that our proposed approach can improve the decoding threshold by 0.05 dB to 0.499 dB depending on the code rate and the order of QAM modulation. Simulation results show that the actual BER improvement varies from 0.09 dB to 0.6 dB with different code-modulation combinations in both single-carrier and OFDM modes. [ABSTRACT FROM AUTHOR]

The Adaptive Belief Propagation (ABP) algorithm was recently proposed by Jiang and Narayanan for the soft decoding of Reed-Solomon (RS) codes. In this paper, simplified versions of this algorithm are investigated for the turbo decoding of product codes. The complexity of the Turbo-oriented Adaptive Belief propagation (TAB) algorithm is significantly reduced by moving the matrix adaptation step outside of the belief propagation iteration loop. A reduced-complexity version of the TAB algorithm that offers a trade-off between performance and complexity is also proposed. Simulation results for the turbo decoding of product codes show that belief propagation based on adaptive parity check matrices is a practical alternative to the currently very popular Chase-Pyndiah algorithm. [ABSTRACT FROM AUTHOR]

Projective geometry is used to decode and represent codes easily. Cameron [1] generated a binary linear code from PG(2,2). In this paper we construct a binary linear code from PG(3,2). Also we give a decoding rule for this code. A simulation study is given to compare this decoding algorithm with maximum likelihood decoding algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a new channel-estimation algorithm based on maximum-likelihood (ML) algorithm for estimation and tracking of the multiple-input-multiple-output (MIMO) channels is presented. The ML algorithm presents the optimum estimation when the exact channel model is known. The derived channel-estimation algorithm is very efficient, with a computational complexity comparable to the least mean square and much lower than the recursive least squares and the Kalman algorithms. The proposed algorithm is analyzed, and the effect of the channel-tracking error is applied as a modifying component for the derived algorithm. The proposed algorithm is simulated for half- and full-rank flat-fading time-varying MIMO channels for the different values of fDT, Eb/No, and training lengths via Monte Carlo simulation technique. The minimum mean-square-error (mmse) joint detector is considered as the detection algorithm. The output of the mmse receiver is considered as the virtual training data in the blind mode of operation: the same as in the decision-directed algorithm. By various simulations, the bit error rate and the mse of tracking the proposed algorithm for different values of fDT, presenting the speed of channel variations, are evaluated and compared with the Kalman filtering approach. By simulating the proposed algorithm for different values of the training length, the minimum training length required for different channel conditions is extracted. [ABSTRACT FROM AUTHOR]

Topological subsystem codes proposed recently by Bombin are quantum error-correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require only the measurement of two-qubit nearest-neighbor operators for error correction. In this paper, we demonstrate that topological subsystem codes (TSCs) can be viewed as generalizations of Kitaev's honeycomb model to 3-valent hypergraphs. This new connection provides a systematic way of constructing TSCs and analyzing their properties. We also derive a necessary and sufficient condition under which a syndrome measurement in a subsystem code can be reduced to measurements of the gauge group generators. Furthermore, we propose and implement some candidate decoding algorithms for one particular TSC assuming perfect error correction. Our Monte Carlo simulations indicate that this code, which we call the five-square code, has a threshold against depolarizing noise of at least 2%. [ABSTRACT FROM AUTHOR]

A novel number theoretic transform called Inverse Gray Robust Symmetrical Number System (IGRSNS) is proposed for error control coding in this paper. IGRSNS is obtained by modifying Robust Symmetrical Number System (RSNS) that was proposed earlier, using Inverse Gray code property. Due to ambiguities present in each residue, RSNS has a short dynamic range (DR) compared to that in other number systems. The short DR of RSNS enables it to be effectively used for error detection without the addition of any redundant modulus as in Redundant Residue Number System. Although RSNS has a large redundant range, its detection ability is not optimal due to the Gray code property associated with it. In an attempt to overcome this limitation, we have proposed Inverse Gray coding to be combined with RSNS in increasing its effectiveness in error detection. The resulting IGRSNS thus inherits properties of both RSNS and Gray code. Analysis and simulations show that IGRSNS has a near-optimal error detection ability. The potential of IGRSNS for error correction is also investigated. Further, a novel error correction algorithm using one redundant modulus is proposed. Simulations show that the proposed algorithm performs well under all cases of single bit errors. [ABSTRACT FROM PUBLISHER]