Uniquely decodable code-division and low-complexity receivers for advanced signal design, multiplexing, and multiple-access communications

In the last decade, wireless communication service has experienced explosive growth while communication technologies have progressed generation by generation. Code-division multiplexing (CDM) or code-division multiple-access (CDMA) is seen as a promising basic technology for 3G/4G cellular communications networks. In such rapidly growing communication systems in which higher number of users share the same channel becomes very challenging problem since it introduces multiple-access interference (MAI).;In this dissertation, we investigate the overloaded code-division multiplexing where the number of multiplexed signals exceeds the code (signature) length L. We propose overloaded code design framework where code set satisfy "errorless" (uniquely decodability) property in noiseless multiplexed transmission. In this proposed framework we aim to identify the maximum number of codes/signatures that can be potentially appended to a Sylvester-Hadamard matrix of order L, while maintaining the errorless code property. We derive formally the maximum number of columns that may be augmented to the Sylverster-Hadamard matrix of order L = 8. It is known that there is no close form formula to identify the maximum number of users K for a any given signature length L. In such system low-complexity multiuser detection techniques are essential. In the noiseless case, we develop a simple algorithm to uniquely decode all signals. To tackle this problem we propose conditional hierarchical criteria for the code (signature) design framework where a simplified maximum-likelihood (SML) detection scheme can be utilized to make CDM systems practically implementable.;In the second part of this work, the problem of list decoding of Reed Solomon codes over the phased burst channels is investigated. We present evidence that the algorithm development by Guruswami and Rudra can also give improvement for more "irregular" burst errors. Specifically, we present simulation results where such soft decoding of Reed-Solomon codes outperforms existing soft decoding algorithms proposed by Koetter and Vardy and, more recently, Das and Vardy on Gilbert-Elliott channels. We also present a theoretical result that for certain Gilbert-Elliott channels, with high probability over the errors, the output list size for list decoding Reed-Solomon codes is one.;Finally, in the third part of this work, we focus on steganalysis, which is the countermeasure of steganography. We propose a passive spread-spectrum steganalysis algorithm to decide the presence or absence of spread-spectrum hidden data in a given image (a binary hypothesis testing problem). Unlike conventional feature-based approaches, we develop an unsupervised (blind) low-complexity approach based on generalized least-squares principles that may enable rapid high-volume image processing. We also consider the problem of blindly extracting data embedded over a wide band in a spectrum (transform) domain of a digital medium (image, audio, video). We first develop a multi-signature iterative generalized least-squares (MIGLS) core procedure to seek unknown data hidden in hosts via multi-signature direct-sequence spread-spectrum embedding. Neither the original host nor the embedding signatures are assumed available. Then, cross-correlation enhanced M-IGLS (CCM-IGLS), a procedure based on statistical analysis of repeated independent M-IGLS processing of the host, is seen to offer most effective hidden message recovery.