Recently, Kundur and Hatzinakos showed that a linear restoration filter designed by using the almost obvious a priori knowledge on the original image, such as (i) nonnegativity of the true image and (ii) the smallest rectangle encompassing the original object, can realize a remarkable performance for a blind image deconvolution problem. In this paper, we propose a new set-theoretic blind image deconvolution scheme based on a recently developed convex projection technique called Hybrid Steepest Descent Method (HSDM), where some partial information can be utilized set-theoretically by parallel projections onto convex sets while the others are incorporated in a cost function to be minimized by a steepest descent method. Numerical comparisons with the standard set-theoretic scheme based on POCS illustrate the effectiveness of the proposed scheme.

Multi-Edge type Low-Density Parity-Check codes (MET-LDPC codes) introduced by Richardson and Urbanke are generalized LDPC codes which can be seen as LDPC codes obtained by concatenating several standard (ir)regular LDPC codes. We prove in this paper that MET-LDPC code ensembles possess a certain symmetry with respect to their Average Coset Weight Distributions (ACWD). Using this symmetry, we drive ACWD of MET-LDPC code ensembles from ACWD of their constituent ensembles.

Irregular Repeat-Accumulate (IRA) codes, introduced by Jin et al., have a linear-time encoding algorithm and their decoding performance is comparable to that of irregular low-density parity-check (LDPC) codes. Meanwhile the authors have introduced detailedly represented irregular LDPC code ensembles specified with joint degree distributions between variable nodes and check nodes. In this paper, by using density evolution method [7],[8], we optimize IRA codes specified with joint degree distributions. Resulting codes have higher thresholds than Jin's IRA codes.

DS-CDMA systems employing long-period PN sequences are becoming a widespread standard of wireless communication systems. However, fast acquisition of long-period PN sequences at a low hardware cost is conventionally a difficult problem. This paper examines a recently proposed fast acquisition algorithm for a class of PN sequences, which includes m and GMW sequences as special cases, under conditions of unknown received RF phase and chip boundary timing. The result shows that under low input (chip) SNR and the required delay estimation accuracy of Tc/Δ, Δ=2,3,…, the mean acquisition time can be considerably reduced compared to other known representative acquisition schemes. Its fast acquisition capability is based on a decomposition of long PN sequences into a number of short ones and achieves a significantly reduced code phase uncertainty of acquisition at relatively small hardware cost, estimated as 2/3 of the equivalent parallel correlators system. It can be applied as a (part of) acquisition scheme of a DS-CDMA system instead of a slow sliding correlator or a costly matched filter schemes.

A lower bound for the generalized Hamming weight of linear codes is proposed. The proposed bound is a generalization of the bound we previously presented and gives good estimate for generalized Hamming weight of Reed-Muller, some one point algebraic geometry, and arbitrary cyclic codes. Moreover the proposed bound contains the BCH bound as its special case. The relation between the proposed bound and conventional bounds is also investigated.

We have proposed in [5] a practical blind channel identification algorithm for the white observation noise. In this paper, we examine the effectiveness of the algorithm given in [5] for the colored observation noise. The proposed algorithm utilizes Gram-Schmidt orthogonalization procedure and estimates (1) the channel order, (2) the noise variance and then (3) the channel impulse response with less computational complexity compared to the conventional algorithms using eigenvalue decomposition. It can be shown through numerical examples that the algorithm proposed in [5] is quite effective in the colored noise case.

In this paper, we study the average symbol and bit-weight distributions for ensembles of non-binary low-density parity-check codes defined on GF(2p). Moreover, we derive the asymptotic exponential growth rate of the weight distributions in the limit of large codelength. Interestingly, we show that the normalized typical minimum distance does not monotonically increase with the size of the field.

This paper proposes an associative memory neural network whose limiting state is the nearest point in a polyhedron from a given input. Two implementations of the proposed associative memory network are presented based on Dykstra's algorithm and a fixed point theorem for nonexpansive mappings. By these implementations, the set of all correctable errors by the network is characterized as a dual cone of the polyhedron at each pattern to be memorized, which leads to a simple amplifying technique to improve the error correction capability. It is shown by numerical examples that the proposed associative memory realizes much better error correction performance than the conventional one based on POCS at the expense of the increase of necessary number of iterations in the recalling stage.

We consider spatially-coupled protograph-based LDPC codes for the three terminal erasure relay channel. It is observed that BP threshold value, the maximal erasure probability of the channel for which decoding error probability converges to zero, of spatially-coupled codes, in particular spatially-coupled MacKay-Neal code, is close to the theoretical limit for the relay channel. Empirical results suggest that spatially-coupled protograph-based LDPC codes have great potential to achieve theoretical limit of a general relay channel.

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.

In this paper, we propose a message passing decoding algorithm which lowers decoding error rates in the error floor regions for non-binary low-density parity-check (LDPC) codes transmitted over the binary erasure channel (BEC) and the memoryless binary-input output-symmetric (MBIOS) channels. In the case for the BEC, this decoding algorithm is a combination with belief propagation (BP) decoding and maximum a posteriori (MAP) decoding on zigzag cycles, which cause decoding errors in the error floor region. We show that MAP decoding on the zigzag cycles is realized by means of a message passing algorithm. Moreover, we extend this decoding algorithm to the MBIOS channels. Simulation results demonstrate that the decoding error rates in the error floor regions by the proposed decoding algorithm are lower than those by the BP decoder.

In this paper, we propose to adopt the asymmetric error correcting code for photon communication systems. The asymmetric error correcting code is an binary code correcting only 10 type transition errors (asymmetric errors). We show the following advantages obtained by employing the asymmetric error correcting code:(i) the codeword error probability is smaller than that of the symmetric error correcting code. (ii) the information rate per photon is larger than that of the symmetric error correcting code. Moreover, for asymmetric error correcting codes, we obtain the lower bounds on the codeword error probability and the upper bounds on the information rate per photon. By using these bounds, we can show that some asymmetric error correcting codes are optimum for these criteria.

In this paper, we explicitly formulate the average weight and the stopping set distributions and their asymptotic exponents of two-edge type LDPC code ensembles. We also show some characteristics such as the symmetry and the conditions for zero of the weight distributions of two code ensembles. Further we investigate the relation between two code ensembles from the perspectives of the weight and stopping set distributions.

In this paper, we derive an upper bound for the average block error probability of a standard irregular low-density parity-check (LDPC) code ensemble under the maximum-likelihood (ML) decoding. Moreover, we show that the upper bound asymptotically decreases polynomially with the code length. Furthermore, when we consider several regular LDPC code ensembles as special cases of standard irregular ones over an additive white Gaussian noise channel, we numerically show that the signal-to-noise ratio (SNR) thresholds at which the proposed bound converges to zero as the code length tends to infinity are smaller than those for a bound provided by Miller et al.. We also give an example of a standard irregular LDPC code ensemble which has a lower SNR threshold than a given regular LDPC code ensemble.

In this paper, we give lower bounds for the generalize Hamming weights of linear codes constructed on affine algebraic varieties. By introducing a number g*, which is determined by a given affine variety, we show that when the order t of generalized Hamming weights is greater than g*, the proposed lower bound agrees with their true generalize Hamming weights. Moreover, if we use the notion of well-behaving, we can obtain a more precise bound. Finally, we compare the proposed bound and the conventional one for algebraic geometric code on the curve Cab.

In this letter, we remark a well-known nonlinear filtering technique realize immediate effect to suppress the influence of the additive measurement noise in the input to a set theoretic linear blind deconvolution scheme. Numerical examples show ε-separating nonlinear pre-filtering techniques work suitably to this noisy blind deconvolution problem.

Low-density parity-check (LDPC) codes are one of the most promising next-generation error-correcting codes. For practical use, efficient methods for encoding of LDPC codes are needed and have to be studied. However, it seems that no general encoding methods suitable for hardware implementation have been proposed so far and for randomly constructed LDPC codes there have been no other methods than the simple one using generator matrices. In this paper we show that some classes of quasi-cyclic LDPC codes based on circulant permutation matrices, specifically LDPC codes based on array codes and a special class of Sridhara-Fuja-Tanner codes and Fossorier codes can be encoded by division circuits as cyclic codes, which are very easy to implement. We also show some properties of these codes.

It is thought that we have generally succeeded in establishing learning algorithms for neural networks, such as the back-propagation algorithm. However two major issues remain to be solved. First, there are possibilities of being trapped at a local minimum in learning. Second, the convergence rate is too slow. Chang and Ghaffar proposed to add a new hidden node, whenever stopping at a local minimum, and restart to train the new net until the error converges to zero. Their method designs newly generated weights so that the new net after introducing a new hidden node has less error than that at the original local minimum. In this paper, we propose a new method that improves their convergence rate. Our proposed method is expected to give a lower system error and a larger error gradient magnitude than their method at a starting point of the new net, which leads to a faster convergence rate. Actually, it is shown through numerical examples that the proposed method gives a much better performance than the conventional Chang and Ghaffar's method.

DS/CDMA systems employing long-period PN sequences are becoming a widespread standard of wireless communication systems. However, fast acquisition of long-period PN sequences at a low hardware cost is conventionally a difficult problem. This paper proposes a new fast acquisition algorithm for a class of PN sequences, which includes m- and GMW sequences as special cases, and shows that the mean (correct) acquisition time can be considerably reduced under input SNR values well below those used in modern DS/CDMA systems. Its fast acquisition capability is based on a decomposition of long PN sequences into a number of short ones and achieves a significantly reduced code phase uncertainty of acquisition at relatively small hardware cost. It can be applied as a (part of) acquisition system of a DS/CDMA system instead of a slow sliding correlator or a costly matched filter.

This paper derives the average symbol and bit weight distributions for the irregular non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we give the exponential growth rates of the average weight distributions in the limit of large code length. We show the condition that the typical minimum distances linearly grow with the code length.