In this paper, we study self-dual cyclic codes of length n over the ring R=Z4[u]/, where n is an odd positive integer. We define a new Gray map φ from R to Z42. It is a bijective map and maintains the self-duality. Furthermore, we give the structures of the generators of cyclic codes and self-dual cyclic codes of odd length n over the ring R. As an application, some self-dual codes of length 2n over Z4 are obtained.

We investigate linear complementary dual (LCD) rank-metric codes in this paper. We construct a class of LCD generalized Gabidulin codes by a self-dual basis of an extension field over the base field. Moreover, a class of LCD MRD codes, which are obtained by Cartesian products of a generalized Gabidulin code, is constructed.

The main purpose of Codemark is to distribute digital contents using offline media. Due to the main purpose of Codemark, Codemark cannot be used on digital images. It has high robustness on only printed images. This paper presents a new color code called Robust Index Code (RIC for short), which has high robustness on JPEG Compression and Resize targeting digital images. RIC embeds a remote database index to digital images so that users can reach to any digital contents. Experimental results, using our implemented RIC encoder and decoder, have shown high robustness on JPEG Comp. and Resize of the proposed codemark. The embedded database indexes can be extracted 100% on compressed images to 30%. In conclusion, it is able to store all the type of digital products by embedding indexes into digital images to access database, which means it makes a Superdistribution system with digital images realized. Therefore RIC has the potential for new Internet image services, since all the images encoded by RIC are possible to access original products anywhere.

Generalized Minimum Distance (GMD) decoding is a well-known soft-decision decoding for linear codes. Previous research on GMD decoding focused mainly on unquantized AWGN channels with BPSK signaling for binary linear codes. In this paper, a study on the design of a 4-level uniform quantizer for GMD decoding is given. In addition, an extended version of a GMD decoding algorithm for a 4-level quantizer is proposed, and the effectiveness of the proposed decoding is shown by simulation.

Non-volatile memories are a promising alternative to memory design but data stored in them still may be destructed due to crosstalk and radiation. The data stored in them can be restored by using error-correcting codes but they require extra bits to correct bit errors. One of the largest problems in non-volatile memories is that they consume ten to hundred times more energy than normal memories in bit-writing. It is quite necessary to reduce writing bits. Recently, a REC code (bit-write-reducing and error-correcting code) is proposed for non-volatile memories which can reduce writing bits and has a capability of error correction. The REC code is generated from a linear systematic error-correcting code but it must include the codeword of all 1's, i.e., 11…1. The codeword bit length must be longer in order to satisfy this condition. In this letter, we propose a method to generate a relaxed REC code which is generated from a relaxed error-correcting code, which does not necessarily include the codeword of all 1's and thus its codeword bit length can be shorter. We prove that the maximum flipping bits of the relaxed REC code is still limited theoretically. Experimental results show that the relaxed REC code efficiently reduce the number of writing bits.

This paper proposes multiple-input multiple-output (MIMO) radar waveforms consisting of Doppler-offset orthogonal complementary codes (DO-OCC) for raising the Doppler resilience of MIMO radar systems. The DO-OCC waveforms have low cross-correlation among multiplexed waves and a low autocorrelation peak sidelobe level (PSL) even in the Doppler shift condition. They are verified by computer simulations and measurements. Computer simulations show that the peak sidelobe ratio (PSR) of the DO-OCC exceeds over 60dB and the desired to undesired signal power ratio (DUR) is over 60dB in the case that the Doppler shift is 0.048 rad per pulse repetition interval (PRI). And through the experimental measurements, it has been verified that the PSR of the DO-OCC is over 40dB and the DUR is over 50dB in the case that Doppler shift is 0.05 rad per PRI and that The DO-OCC waveforms enable to maintain the direction of arrival (DOA) estimation accuracy for moving targets as almost same as the one for static targets. The results prove the effectiveness of the proposed MIMO waveforms in achieving Doppler tolerance while maintaining orthogonality and autocorrelation properties.

In mobile and wireless networks, controlling data delivery latency is one of open problems due to the stochastic nature of wireless channels, which are inherently unreliable. This paper explores how the current best-effort throughput-oriented wireless services might evolve into latency-sensitive enablers of new mobile applications such as remote three-dimensional (3D) graphical rendering for interactive virtual/augmented-reality overlay. Assuming that the signal propagation delay and achievable throughput meet the standard latency requirements of the user application, we examine the idea of trading excess/federated bandwidth for the elimination of non-negligible delay of data re-ordering, caused by temporal transmission failures and buffer overflows. The general system design is based on (i) spatially diverse data delivery over multiple paths with uncorrelated outage likelihoods; and (ii) forward packet-loss protection (FPP), creating encoding redundancy for proactive recovery of intolerably delayed data without end-to-end retransmissions. Analysis and evaluation are based on traces of real life traffic, which is measured in live carrier-grade long term evolution (LTE) networks and campus WiFi networks, due to no such system/environment yet to verify the importance of spatial diversity and encoding redundancy. Analysis and evaluation reveal the seriousness of the latency problem and that the proposed FPP with spatial diversity and encoding redundancy can minimize the delay of re-ordering. Moreover, a novel FPP effectiveness coefficient is proposed to explicitly represent the effectiveness of EPP implementation.

Erasure codes have been considered as one of the most promising techniques for data reliability enhancement and storage efficiency in modern distributed storage systems. However, erasure codes often suffer from a time-consuming coding process which makes them nearly impractical. The opportunity to solve this problem probably rely on the parallelization of erasure-code-based application on the modern multi-/many-core processors to fully take advantage of the adequate hardware resources on those platforms. However, the complicated data allocation and limited I/O throughput pose a great challenge on the parallelization. To address this challenge, we propose a general multi-threaded parallel coding approach in this work. The approach consists of a general multi-threaded parallel coding model named as MTPerasure, and two detailed parallel coding algorithms, named as sdaParallel and ddaParallel, respectively, adapting to different I/O circumstances. MTPerasure is a general parallel coding model focusing on the high level data allocation, and it is applicable for all erasure codes and can be implemented without any modifications of the low level coding algorithms. The sdaParallel divides the data into several parts and the data parts are allocated to different threads statically in order to eliminate synchronization latency among multiple threads, which improves the parallel coding performance under the dummy I/O mode. The ddaParallel employs two threads to execute the I/O reading and writing on the basis of small pieces independently, which increases the I/O throughput. Furthermore, the data pieces are assigned to the coding thread dynamically. A special thread scheduling algorithm is also proposed to reduce thread migration latency. To evaluate our proposal, we parallelize the popular open source library jerasure based on our approach. And a detailed performance comparison with the original sequential coding program indicates that the proposed parallel approach outperforms the original sequential program by an extraordinary speedups from 1.4x up to 7x, and achieves better utilization of the computation and I/O resources.

In this paper, a study of a sufficient condition on the optimality of a decoded codeword of soft-decision decodings for binary linear codes is shown for a quantized case. A typical uniform 4-level quantizer for soft-decision decodings is employed for the analysis. Simulation results on the (64,42,8) Reed-Muller code indicates that the condition is effective for SN ratios at 3[dB] or higher for any iterative style optimum decodings.

The separating redundancy is an important concept in the analysis of the error-and-erasure decoding of a linear block code using a parity-check matrix of the code. In this letter, we derive new constructive upper bounds on the second separating redundancies of low-density parity-check (LDPC) codes constructed from projective and Euclidean planes over the field Fq with q even.

Concatenated zigzag (CZ) codes are classified as one kind of parallel-concatenated codes with powerful performance and low complexity. This kind of codes has flexible implementation methods and a good application prospect. We propose a modified turbo-type decoder and adaptive extrinsic information scaling method based on the Max-Log-APP (MLA) algorithm, which can provide a performance improvement also under the relatively low decoding complexity. Simulation results show that the proposed method can effectively help the sub-optimal MLA algorithm to approach the optimal performance. Some contrasts with low-density parity-check (LDPC) codes are also presented in this paper.

By tracking the changing rate of hard decisions during every two consecutive iterations of the alternating direction method of multipliers (ADMM) penalized decoding, an efficient early termination (ET) criterion is proposed to improve the convergence rate of ADMM penalized decoder for low-density parity-check (LDPC) codes. Compared to the existing ET criterion for ADMM penalized decoding, the proposed method can reduce the average number of iterations significantly at low signal-to-noise ratios with negligible performance degradation.

Codes over permutations and multipermutations have received considerable attention since the rank modulation scheme is presented for flash memories. Deletions in multipermutations often occur due to data synchronization errors. Based on the interleaving of several single-deletion-correcting multipermutation codes, we present a construction of multipermutation codes for correcting a burst of at most t deletions with shift magnitude one for t ≥2. The proposed construction is proved with including an efficient decoding method. A calculation example is provided to validate the construction and its decoding method.

Deep neural network (DNN)-based speech synthesis can produce more natural synthesized speech than the conventional HMM-based speech synthesis. However, it is not revealed whether the synthesized speech quality can be improved by utilizing a multi-speaker speech corpus. To address this problem, this paper proposes DNN-based speech synthesis using speaker codes as a method to improve the performance of the conventional speaker dependent DNN-based method. In order to model speaker variation in the DNN, the augmented feature (speaker codes) is fed to the hidden layer(s) of the conventional DNN. This paper investigates the effectiveness of introducing speaker codes to DNN acoustic models for speech synthesis for two tasks: multi-speaker modeling and speaker adaptation. For the multi-speaker modeling task, the method we propose trains connection weights of the whole DNN using a multi-speaker speech corpus. When performing multi-speaker synthesis, the speaker code corresponding to the selected target speaker is fed to the DNN to generate the speaker's voice. When performing speaker adaptation, a set of connection weights of the multi-speaker model is re-estimated to generate a new target speaker's voice. We investigated the relationship between the prediction performance and architecture of the DNNs through objective measurements. Objective evaluation experiments revealed that the proposed model outperformed conventional methods (HMMs, speaker dependent DNNs and multi-speaker DNNs based on a shared hidden layer structure). Subjective evaluation experimental results showed that the proposed model again outperformed the conventional methods (HMMs, speaker dependent DNNs), especially when using a small number of target speaker utterances.

This letter presents numerical results of lossy source coding for non-uniformly distributed binary source with trellis codes. The results show how the performance of trellis codes approaches the rate-distortion function in terms of the number of states.

In this paper, a weighted multiple bit flipping (WMBF) algorithman for decoding low-density parity-check (LDPC) codes is proposed first. Then the improved WMBF algorithm which we call the efficient weighted bit-flipping (EWBF) algorithm is developed. The EWBF algorithm can dynamically choose either multiple bit-flipping or single bit-flipping in each iteration according to the log-likelihood ratio of the error probability of the received bits. Thus, it can efficiently increase the convergence speed of decoding and prevent the decoding process from falling into loop traps. Compared with the parallel weighted bit-flipping (PWBF) algorithm, the EWBF algorithm can achieve significantly lower computational complexity without performance degradation when the Euclidean geometry (EG)-LDPC codes are decoded. Furthermore, the flipping criterion does not require any parameter adjustment.

In this paper, a study on the design and implementation of uniform 4-level quantizers for soft-decision decodings for binary linear codes is shown. Simulation results on quantized Viterbi decoding with a 4-level quantizer for the (64,42,8) Reed-Muller code show that the optimum stepsize, which is derived from the cutoff rate, gives an almost optimum error performance. In addition, the simulation results show that the case where the number of optimum codewords is larger than the one for a received sequence causes non-negligible degradation on error performance at high SN ratios of Eb/N0.

This paper studies the zero error capacity of the Nearest Neighbor Error (NNE) channels with a multilevel alphabet. In the NNE channels, a transmitted symbol is a d-tuple of elements in {0,1,2,...,l-1}. It is assumed that only one element error to a nearest neighbor element in a transmitted symbol can occur. The NNE channels can be considered as a special type of limited magnitude error channels, and it is closely related to error models for flash memories. In this paper, we derive a lower bound of the zero error capacity of the NNE channels based on a result of the perfect Lee codes. An upper bound of the zero error capacity of the NNE channels is also derived from a feasible solution of a linear programming problem defined based on the confusion graphs of the NNE channels. As a result, a concise formula of the zero error capacity is obtained using the lower and upper bounds.

Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes [4]-[8], [10]. In those works the focus is on full privacy and full reconstruction. In this paper we analyze additional parameters describing the asymptotic behavior of partial information leakage and possibly also partial reconstruction giving a more complete picture of the access structure for sequences of linear ramp secret sharing schemes. Our study involves a detailed treatment of the (relative) generalized Hamming weights of the considered codes.

In this paper, we propose a construction of non-binary WOM (Write-Once-Memory) codes for WOM storages such as flash memories. The WOM codes discussed in this paper are fixed rate WOM codes where messages in a fixed alphabet of size M can be sequentially written in the WOM storage at least t*-times. In this paper, a WOM storage is modeled by a state transition graph. The proposed construction has the following two features. First, it includes a systematic method to determine the encoding regions in the state transition graph. Second, the proposed construction includes a labeling method for states by using integer programming. Several novel WOM codes for q level flash memories with 2 cells are constructed by the proposed construction. They achieve the worst numbers of writes t* that meet the known upper bound in the range 4≤q≤8, M=8. In addition, we constructed fixed rate non-binary WOM codes with the capability to reduce ICI (inter cell interference) of flash cells. One of the advantages of the proposed construction is its flexibility. It can be applied to various storage devices, to various dimensions (i.e, number of cells), and various kind of additional constraints.