Uniquely Decodable Ternary Codes for Synchronous CDMA Systems

2011 18th International Conference on Telecommunications, 2011

Recently, a new class of binary codes for overloaded CDMA systems are proposed that not only has the ability of errorless communication but also suitable for detecting active users. These codes are called COWDA [1]. In [1], a Maximum Likelihood (ML) decoder is proposed for this class of codes. Although the proposed scheme of coding/decoding show impressive performance, the decoder can be improved. In this paper by assuming more practical conditions for the traffic in the system, we suggest an algorithm that increases the performance of the decoder several orders of magnitude (the Bit-Error-Rate (BER) is divided by a factor of about in some ⁄ 's). The algorithm supposes the Poison distribution for the time of activation/deactivation of the users.

A new non-binary decoding method, which is called Yaletharatalhussein decoding algorithm, is designed and implemented for decoding non-binary convolutional codes which is based on the trellis diagram representing the convolutional encoder. Yaletharatalhussein decoding algorithm outperforms the Viterbi algorithm and other algorithms in its simplicity, very small computational complexity, decoding reliability for high states TCM codes that suitable for Fourth-Generation (4G), decreasing errors with increasing word length, and easy to implement with real-time applications. The proposed Yaletharatalhussein decoding algorithm deals with non-binary error control coding of the convolutional and TCM codes. Convolutional codes differ from block codes in that a block code takes a fixed message length and encodes it, whereas a convolutional code can encode a continuous stream of data, and a hard-decision decoding can easily be realized using the Yaletharatalhussein algorithm. The idea of non-binary codes has been extended for symbols defined over rings of integers, which outperform binary codes with only a small increase in decoding complexity. The simulation results show that the performance of the nonbinary TCM-based Yaletharatalhussein algorithm outperforms the binary and non-binary decoding methods.

2009 IEEE International Conference on Communications, 2009

In this paper we introduce a new class of codes for over-loaded synchronous wireless CDMA systems which increases the number of users for a fixed number of chips without introducing any errors. In addition these codes support active user detection. We derive an upper bound on the number of users with a fixed spreading factor. Also we propose an ML decoder for a subclass of these codes that is computationally implementable. Although for our simulations we consider a scenario that is worse than what occurs in practice, simulation results indicate that this coding/decoding scheme is robust against additive noise. As an example, for 64 chips and 88 users we propose a coding/decoding scheme that can obtain an arbitrary small probability of error which is computationally feasible and can detect active users. Furthermore, we prove that for this to be possible the number of users cannot be beyond 230.

In this paper, we study binary and ternary matrices that are used for CDMA applications that are injective on binary or ternary user vectors. In other words, in the absence of additive noise, the interference of overloaded CDMA can be removed completely. Some new algorithms are proposed for constructing such matrices. Also, using an information theoretic approach, we conjecture the extent to which such CDMA matrix codes exist. For overloaded case, we also show that some of the codes derived from our algorithms perform better than the binary Welch Bound Equality codes; the decoding is ML but of low complexity.

International Journal of Computer Applications, 2015

Pulse Compression Sequence is wide utilized inthe field of radar, communication to extend the range resolution. Sequences with good discriminating and merit factor are useful for channel estimation, radar and spread spectrum communication application. Binary sequence has the limitation that the compression ratio is small. Ternary alphabets are suggested as an alternative. The design of ternary codes with good merit factor and discriminating factor can be considered as a nonlinear multivariable mathematical problem which is difficult find a optimal solution. To get the solution for the this problem many global optimization algorithms like Simulated Annealing Algorithm(SA), Genetic Algorithm (GA), Tunneling algorithm (TA) and particle swarm optimization algorithm (PSO) could be used.Further a set of pulse compression sequence are required for spread spectrum and CDMA application such that the individual autocorrelation function of each sequence is like an impulse and the cross correlation between any two sequences in the set must be zero for all lags unfortunately.In this paper, it is proposed to use a new method of algorithm for the design of best ternary codes sets for various lengths by using Modified Simulated Annealing Algorithm. The general features such as global convergence and robustness of the statistical algorithm are revealed.

IEEE Journal on Selected Areas in Communications, 2001

Lecture Notes in Computer Science, 2006

Error correcting output codes (ECOC) represent a successful extension of binary classifiers to address the multiclass problem. Lately, the ECOC framework was extended from the binary to the ternary case to allow classes to be ignored by a certain classifier, allowing in this way to increase the number of possible dichotomies to be selected. Nevertheless, the effect of the zero symbol by which dichotomies exclude certain classes from consideration has not been previously enough considered in the definition of the decoding strategies. In this paper, we show that by a special treatment procedure of zeros, and adjusting the weights at the rest of coded positions, the accuracy of the system can be increased. Besides, we extend the main state-of-art decoding strategies from the binary to the ternary case, and we propose two novel approaches: Laplacian and Pessimistic Beta Density Probability approaches. Tests on UCI database repository (with different sparse matrices containing different percentages of zero symbol) show that the ternary decoding techniques proposed outperform the standard decoding strategies.

IEEE Transactions on Signal Processing, 2006

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010

A common way to model multiclass classification problems is to design a set of binary classifiers and to combine them. Error-Correcting Output Codes (ECOC) represent a successful framework to deal with these type of problems. Recent works in the ECOC framework showed significant performance improvements by means of new problem-dependent designs based on the ternary ECOC framework. The ternary framework contains a larger set of binary problems because of the use of a "do not care" symbol that allows us to ignore some classes by a given classifier. However, there are no proper studies that analyze the effect of the new symbol at the decoding step. In this paper, we present a taxonomy that embeds all binary and ternary ECOC decoding strategies into four groups. We show that the zero symbol introduces two kinds of biases that require redefinition of the decoding design. A new type of decoding measure is proposed, and two novel decoding strategies are defined. We evaluate the state-of-the-art coding and decoding strategies over a set of UCI Machine Learning Repository data sets and into a real traffic sign categorization problem. The experimental results show that, following the new decoding strategies, the performance of the ECOC design is significantly improved.

IEEE Transactions on Information Theory, 2000

In this paper we introduce a new class of codes for over-loaded synchronous wireless and optical CDMA systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of a binary over-loaded CDMA are derived that can predict the existence of such over-loaded codes. We also propose a simplified maximum likelihood method for decoding these types of over-loaded codes. Although a high percentage of the over-loading factor 3 degrades the system performance in noisy channels, simulation results show that this degradation is not significant. More importantly, for moderate values of ‫ܧ‬ ܰ Τ (in the range of -ͳͲ dB) or higher, the proposed codes perform much better than the binary Welch bound equality sequences.