New decoding algorithms for binary linear codes based on the concave-convex procedure are presented. Numerical experiments show that the proposed decoding algorithms surpass Belief Propagation (BP) decoding in error performance. Average computational complexity of one of the proposed decoding algorithms is only a few times greater than that of the BP decoding.

The history of forward error correction in optical communications is reviewed. The various types of FEC are classified as belonging to three generations. The first generation FEC represents the first to be successful in submarine systems, when the use of RS(255, 239) became widespread as ITU-T G.975, and also as G.709 for terrestrial systems. As WDM systems matured, a quest began for a stronger second generation FEC. Several types of concatenated code were proposed for this, and were installed in commercial systems. The advent of third-generation FEC opened up new vistas for the next generation of optical communication systems. Thanks to soft decision decoding and block turbo codes, a net coding gain of 10.1 dB has been demonstrated experimentally. That brought us a number of positive impacts on existing systems. Each new generation of FEC was compared in terms of the ultimate coding gain. The Shannon limit was discussed for hard or soft decision decoding. Several functionalities employing the FEC framing were introduced, such as overall wrapping by the FEC frame enabling the asynchronous multiplexing of different clients' data. Fast polarization scrambling with FEC was effective in mitigating polarization mode dispersion, and the error monitor function proved useful for the adaptive equalization of both chromatic dispersion and PMD.

We present a simple decoding algorithm that modifies soft bit-flipping algorithm for decoding LDPC codes. In our method, a new parameter is explored to distinguish the variables (symbols) belonging to the same number of unsatisfied constraints. A token is also assigned in the method to avoid repeated flipping of the same variable, rather than using a constant taboo length. Our scheme shows a similar computational load as the taboo-based algorithm, while having a similar decoding performance as the belief propagation algorithm.

This paper presents a novel decoding algorithm for turbo codes, in which the likelihood values for redundant parts are updated in order for those values to become more reliable. A criterion for updating the redundant likelihood values is proposed, which is based on the comparisons of the channel values with the re-generated values by the soft-input and soft-output encoders. It is shown that the proposed method can improve the error correcting capabilities, i.e., the improvement of BER/BLER performance and the achievable BER limit.

This letter proposes an efficient and simple stopping criterion for turbo decoding, which is derived by observing the behavior of log-likelihood ratio (LLR) values. Based on the behavior, the proposed criterion counts the number of absolute LLR values less than a threshold and the number of hard decision 1's in order to complete the iterative decoding procedure. Simulation results show that the proposed approach achieves a reduced number of iterations while maintaining similar BER/FER performance to the previous criteria.

This paper investigates a random-interleaver-based approach to space-time coding. The basic principle is to employ a good forward error correction (FEC) code and transmit randomly interleaved codewords over an antenna array. A low-cost estimation technique is considered. The complexity involved grows only linearly with the number of transmit antennas. Near-capacity performance can be achieved with moderate complexity.

This paper is concerned with the signal processing aspects of the recently proposed interleave-division multiple-access (IDMA) scheme. We propose several low-cost detection algorithms to solve the problems of multiple-access, cross-antenna and intersymbol interference (ISI). The complexities (per user) of these algorithms are very low and increase either linearly or quadratically with the number of paths. It is shown that an IDMA system with a rate- 16-state convolutional code and a length-8 spreading sequence can support more than 100 users in a multipath fading channel with two receive antennas. This clearly indicates the great potential of IDMA systems.

One of the categories of decoding techniques for DFT codes in erasure channels is the class of iterative algorithms. Iterative algorithms can be considered as kind of alternating mapping methods using the given information in a repetitive way. In this paper, we propose a new iterative method for decoding DFT codes. It will be shown that the proposed method outperforms the well-known methods such as Wiley/Marvasti, and ADPW methods in the decoding of DFT codes in erasure channels.

This paper presents a novel decoding strategy called combined iterative demapping/decoding (CIDD), for coded M-ary biorthogonal keying-based direct sequence ultra-wideband (MBOK DS-UWB) systems. A coded MBOK DS-UWB system consists of a convolutional encoder, an interleaver, and an MBOK DS-UWB pulse mapper. CIDD improves the error rate performance of MBOK DS-UWB systems by applying the turbo principle to the demapping and decoding processes at the receiver side. To develop the CIDD, a soft-in/soft-out MBOK demapping algorithm, based on the max-log-MAP algorithm, was derived. Simulation results showed that using CIDD siginificantly improved the error rate performance of both static and multipath fading channels. It was also shown that the computational complexity of CIDD is comparable to that of the Viterbi decoding used in [133,171]8 conventional convolutional coding.

Iterative decodings used for turbo codes, concatenated codes and LDPC codes have been the main current of Coding Theory. Many researches have been done to improve the structure, algorithms and so on. But, the iterative process itself was not so much improved. On the other hand, in the field of nonlinear analysis, various iterative methods have been studied for nonlinear mappings. We consider the iterative decodings as nonlinear discrete dynamical systems in mathematics and apply iterative processes called Mann type iteration to the iterative decoding process. We will show, by using monotone operator theory, that the proposed method has more extensive stable domain than that of the conventional iterative process. Moreover, we will see the effect of proposed method in computer simulations.

Density evolution has recently been used to analyze the iterative decoding of Low Density Parity Check (LDPC) codes, Turbo codes, and Serially Concatenated Convolutional Codes (SCCC). The density evolution technique makes it possible to explain many characteristics of iterative decoding including convergence of performance and preferred structures for the constituent codes. While the analytic density evolution methods were applied to LDPC codes, the simulation based density evolution methods were used for Turbo codes and SCCC due to analytic difficulties. In this paper, several density evolution ideas in the literature are used to analyze common code structures and it is shown that those ideas yield consistent results. In order to do that, we derive expressions for density evolution of SCCC with a simple 2-state constituent code. The analytic expressions are based on the sum-product and min-sum algorithms, and the thresholds are evaluated for both message passing algorithms. Particularly, for the min-sum algorithm, the density evolution with Gaussian approximation is derived and used to analyze the effect of scaling soft information. The scaling of extrinsic information slows down the convergence of soft information or avoids an overestimation effect of it and results in better performance, and its gain is maximized in particular constituent codes. Similar approaches are made for LDPC code. We show that the scaling gain is noticeable in the LDPC code as well. This scaling gain is analyzed with both density evolution and simulation performance. The expected scaling gain by density evolution matches well with the achievable scaling gain from simulation results. These results can be extended to the irregular LDPC codes based on the degree distribution for the min-sum algorithm. All density evolution algorithms used in this paper are based on the Gaussian approximation for the exchanged messages.

Fading in mobile satellite communications severely degrades the performance of data transmission. It is commonly modeled with non-frequency selective Rayleigh fading. For this type of channel, a new structure for a bit-interleaved coded modulation (BICM) scheme is presented and evaluated to determine its effectiveness compared to previously proposed schemes. This scheme is referred to as rate-compatible punctured BICM (RCP-BICM), in that its BICM encoder is able to yield a wide range of data rates by using a punctured convolutional code obtained by periodically perforating parity bits from the output of a low-rate-1/2 systematic convolutional code. A trellis-coded modulation (TCM) scheme and a turbo TCM (TTCM) scheme are discussed and evaluated for comparison with the RCP-BICM scheme. Simulation results demonstrate that the RCP-BICM scheme with hard-decision iterative decoding is superior to the TCM scheme by 3 dB at a bit error rate (BER) of 10-5 over an Rayleigh fading channel, and comes at a BER of 10-5 within 1 dB of the TCM scheme over an additive white Gaussian noise (AWGN) channel.

The codes by the u/u+v construction have the extended error capacity for additional Hamming weight. It is a simple way to construct a large size block code using smaller ones. In this letter, low density parity check (LDPC) codes on u/u+v construction are investigated. Consequently, the study can enrich the family of LDPC codes and provide some special LDPC implementations.

Given the importance of the traffic on modern communication networks, advanced error correction methods are needed to overcome the changes expected in channel quality. Conventional countermeasures that use high dimensionality parity codes often fail to provide sufficient error correction capability. We propose a parity code with high dimensionality that is iteratively decoded. It provides better error correcting capability than conventional decoding methods. The proposal uses the steepest descent method to increase code bit reliability and the coherency between parities and code bits gradually. Furthermore, the quantization of the decoding algorithm is discussed. It is found that decoding with quantization can keep the error correcting capability high.

In this letter, we propose (1) a new sub-optimum minimum distance search (sub-MDS), whose search complexity is reduced considerably compared with optimum MDSs and (2) a termination criterion, called near optimality condition, to reduce the average number of decoding iterations with little degradation of error performance for the proposed decoding using sub-MDS iteratively. Consequently, the decoding algorithm can be applied to longer codes with feasible complexity. Simulation results for several Reed-Muller (RM) codes of lengths 256 and 512 are given.

We consider a soft-decision iterative bounded distance decoding algorithm for binary linear block codes. In the decoding algorithm, bounded distance decodings are carried out with respect to successive input words, called the search centers. A search center is the sum of the hard-decision sequence of a received sequence and a sequence in a set of test patterns which are generated beforehand. This set of test patterns has influence on the error performance of the decoding algorithms as simulation results show. In this paper, we propose a construction method of a set of candidate test patterns and a selection method of test patterns based on an introduced measure of effectiveness of test patterns. For several BCH codes of lengths 127, 255 and 511, we show the effectiveness of the proposed method by simulation.

In this letter, we show the effectiveness of a double-loop algorithm based on the concave-convex procedure (CCCP) in decoding linear codes. For this purpose, we numerically compare the error performance of CCCP-based decoding algorithm with that of a conventional iterative decoding algorithm based on belief propagation (BP). We also investigate computational complexity and its relation to the error performance.

In this paper, an iterative decoding algorithm for channels with additive linear dynamical noise is presented. The proposed algorithm is based on the tightly coupled two inference algorithms: the sum-product algorithm which infers the information symbols of an low density parity check (LDPC) code and the Kalman smoothing algorithm which infers the channel states. The linear dynamical noise are the noise generated from a linear dynamical system. We often encounter such noise (i.e., additive colored noise) in practical communication and storage systems. The conventional iterative decoding algorithms such as the sum-product algorithm cannot derive full potential of turbo codes nor LDPC codes over such a channel because the conventional algorithms are designed under the independence assumption on the noise. Several simulations have been performed to assess the performance of the proposed algorithm. From the simulation results, it can be concluded that the Kalman smoothing algorithm deserves to be implemented in a decoder when the linear dynamical part of the linear dynamical noise is dominant rather than the white Gaussian noise part. In such a case, the performance of the proposed algorithm is far superior to that of the conventional algorithm.

This letter contains our proposal for a new iterative decoding algorithm for Turbo coded V-BLAST system. The proposed algorithm is based on maximum a posteriori (MAP) decision criterion. In a V-BLAST system concatenated with Turbo codes, the extrinsic information from the soft output channel decoder can be utilized as a priori probability, making it possible to apply MAP decision criteria to the V-BLAST decoding process. The MAP decision criterion is applied to the V-BLAST ordering and slicing procedure, resulting in a considerable gain in bit error performance. As the iteration rate increases, the proposed system exhibits performance similar to that of system with ideal sliced.

A parity check matrix for a binary linear code defines a bipartite graph (Tanner graph) which is isomorphic to a subgraph of a factor graph which explains a mechanism of the iterative decoding based on the sum-product algorithm. It is known that this decoding algorithm well approximates MAP decoding, but degradation of the approximation becomes serious when there exist cycles of short length, especially length 4, in Tanner graph. In this paper, based on the generating idempotents, we propose some methods to design parity check matrices for cyclic codes which define Tanner graphs with no cycles of length 4. We also show numerically error performance of cyclic codes by the iterative decoding implemented on factor graphs derived from the proposed parity check matrices.