Serial Turbo Codes Research Articles

Crypto-Watermarking Algorithm Using Weber’s Law and AES: A View to Transfer Safe Medical Image

We propose a novel method for medical image watermarking in the DCT domain using the AES encryption algorithm. First, we decompose the original medical image into subblocks of 8 × 8. Besides, we apply the DCT and the quantization, respectively, to each subblock. However, in the DCT domain, an adequate choice of the DCT coefficients according to the quantization table in the middle frequencies band is performed. After that, we embed the patient’s data into the corresponding medical image. The insertion step is carried out just after the quantization phase. To increase the robustness, we encrypt the watermarked medical images by using the AES algorithm based on chaotic technique. Arnold’s cat map is used to shuffle the pixel values, and a chaotic Henon map is utilized to generate an aleatory sequence for the AES algorithm. The shuffled watermarked image is encrypted using the modified AES algorithm. The constant of Weber is used to choose the suitable visibility factor for embedding a watermark with high robustness. To control identification, after application of attacks, we use the serial turbo code for correction of the watermark to recover the data inserted. The average peak signal-to-noise ratio (PSNR) of the medical images obtained is 61,7769 dB. Experimental results demonstrate the robustness of the proposed schema against various types of attacks.

Algorithms for noncoherent iterative reception of signals based on serial turbo codes and Walsh signals during transmission over nonstationary channels

The results of simulating the algorithms developed for noncoherent iterative reception of signals based on highly redundant serial turbo codes and Walsh signal ensembles are presented. It is assumed that transmission is carried out over nonstationary channels.

Combining watermarking and encryption algorithm for medical image safe transfer: method based on DCT

A novel method for watermarking and encryption of medical image based on the DCT is presented. Medical data, such as the patients' private information is embedded into the corresponding medical image. After that, the watermarked medical images are encrypted by using the AES and the RSA encryption Algorithm to increase the robustness. Our method uses the standard JPEG compression for the embedding of patients' private data. The insertion block is inserted just after the DCT phase. To control identification and eventually the correction of the watermark, it should be noted that we used the serial turbo code to recover the data inserted. The proposed system is tested against several attacks, such as compression, noises, filtering and geometric transformation. Experiments and analyses show that low distortion and high robustness have been achieved in the process of watermarking, and, at the same time, elevated security has been acquired in the encryption phase.

The Performance of Serial Turbo Codes Does Not Concentrate

Minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed. It is shown that, for a fraction of interleavers approaching one as the block-length grows large, the minimum distance of serial turbo codes grows as a positive power of their block-length, while their error probability decreases exponentially fast in some positive power of their block-length, on sufficiently good memoryless channels. Such a typical code behavior contrasts the performance of the average serial turbo code, whose error probability is dominated by an asymptotically negligible fraction of poorly performing interleavers, and decays only as a negative power of the block-length. The analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code, whose scaling law is shown to depend both on the free distance of its outer constituent encoder, which determines the exponent of its sub-linear growth in the block-length, and on the effective free distance of its inner constituent encoder. The latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two, and appears as a linear scaling factor for the minimum distance of the typical serial turbo code. Hence, despite the lack of concentration of the maximum likelihood error probability around its expected value, the main design parameters suggested by the average-code analysis turn out to characterize also the performance of the typical serial turbo code. By showing for the first time that the typical serial turbo code's minimum distance scales linearly in the effective free distance of the inner constituent encoder, the presented results generalize, and improve upon, the probabilistic bounds of Kahale and Urbanke, as well as the deterministic upper bound of Bazzi, Mahdian, and Spielman, where only the dependence on the outer encoder's free distance was proved.

Coding and Detection for Rectangular-Grain TDMR Models

This paper studies the performance of a serial turbo code on two simplified rectangular-grain models of recording media for two-dimensional (2-D) magnetic recording at a density of more than 0.5 bits/grain. We derive one-dimensional (1-D) and 2-D rectangular-grain media models and from these present finite-state-machine (FSM) representations. From the FSM for the 1-D model we computed achievable information rates assuming independent and uniformly distributed (i.u.d.) binary inputs. From the (approximate) FSM for the 2-D model, we present a detector. We then present a serial turbo code architecture with constituent convolutional codes that is capable of achieving 80% of i.u.d. capacity for the 1-D model and 65% of the average of published upper and lower bounds on capacity for the 2-D model. We also present schemes which combine the advantages of an (inner) repetition code and an (outer) serial turbo code. One such scheme cleverly arranges the three bits in each three-fold repetition into the shape of an “L”. This obviates the need for a sequence detector and converts the 2-D channel model into an equivalent binary symmetric channel.

Serial turbo codes with a low complexity of reception algorithms

The results of investigating the developed efficient procedures of iterative reception of serial turbo codes based on a simple convolutional code with two possible states of a code trellis are presented.

Quantum Serial Turbo Codes

In this paper, we present a theory of quantum serial turbo codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum low-density parity-check (LDPC) codes. First, the Tanner graph used for decoding is free of 4-cycles that deteriorate the performances of iterative decoding. Second, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular, its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoders have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be noncatastrophic and nonrecursive. While the resulting families of turbo codes have bounded minimum distance, from a pragmatic point of view, the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes. With well-chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases.

Analysis of Serial Turbo Codes over Abelian Groups for Symmetric Channels

In this paper we study serial turbo interconnections of Abelian group codes to be used on symmetric channels. Particular attention is devoted to AWGN channel with input restricted to $m$-PSK constellation with corresponding group structure $\mathbb{Z}_m$. We establish the exact asymptotic decay of the average symbol and word error probabilities when the interleaver length goes to infinity (interleaver gain). Moreover, we give a detailed characterization of the distance parameter characterizing the behavior for the signal-to-noise ratio going to infinity (effective free distance). Some of our results are new also in the binary context; in particular, the lower bound to the error probability decay.

An Efficient SF-ISF Approach for the Slepian-Wolf Source Coding Problem

A simple but powerful scheme exploiting the binning concept for asymmetric lossless distributed source coding is proposed. The novelty in the proposed scheme is the introduction of a syndrome former (SF) in the source encoder and an inverse syndrome former (ISF) in the source decoder to efficiently exploit an existing linear channel code without the need to modify the code structure or the decoding strategy. For most channel codes, the construction of SF-ISF pairs is a light task. For parallelly and serially concatenated codes and particularly parallel and serial turbo codes where this appear less obvious, an efficient way for constructing linear complexity SF-ISF pairs is demonstrated. It is shown that the proposed SF-ISF approach is simple, provenly optimal, and generally applicable to any linear channel code. Simulation using conventional and asymmetric turbo codes demonstrates a compression rate that is only 0.06 bit/symbol from the theoretical limit, which is among the best results reported so far.

Design of Efficiently Encodable Moderate-Length High-Rate Irregular LDPC Codes

This paper presents a new class of irregular low-density parity-check (LDPC) codes of moderate length (10/sup 3//spl les/n/spl les/10/sup 4/) and high rate (R/spl ges/3/4). Codes in this class admit low-complexity encoding and have lower error-rate floors than other irregular LDPC code-design approaches. It is also shown that this class of LDPC codes is equivalent to a class of systematic serial turbo codes and is an extension of irregular repeat-accumulate codes. A code design algorithm based on the combination of density evolution and differential evolution optimization with a modified cost function is presented. Moderate-length, high-rate codes with no error-rate floors down to a bit-error rate of 10/sup -9/ are presented. Although our focus is on moderate-length, high-rate codes, the proposed coding scheme is applicable to irregular LDPC codes with other lengths and rates.

Soft and Joint Source-Channel Decoding of Quasi-Arithmetic Codes

The issue of robust and joint source-channel decoding of quasi-arithmetic codes is addressed. Quasi-arithmetic coding is a reduced precision and complexity implementation of arithmetic coding. This amounts to approximating the distribution of the source. The approximation of the source distribution leads to the introduction of redundancy that can be exploited for robust decoding in presence of transmission errors. Hence, this approximation controls both the trade-off between compression efficiency and complexity and at the same time the redundancy (excess rate) introduced by this suboptimality. This paper provides first a state model of a quasi-arithmetic coder and decoder for binary and M-ary sources. The design of an error-resilient soft decoding algorithm follows quite naturally. The compression efficiency of quasi-arithmetic codes allows to add extra redundancy in the form of markers designed specifically to prevent desynchronization. The algorithm is directly amenable for iterative source-channel decoding in the spirit of serial turbo codes. The coding and decoding algorithms have been tested for a wide range of channel signal-to-noise ratios (SNRs). Experimental results reveal improved symbol error rate (SER) and SNR performances against Huffman and optimal arithmetic codes.

Soft decoding and synchronization of arithmetic codes: application to image transmission over noisy channels

This paper addresses the issue of robust and joint source-channel decoding of arithmetic codes. We first analyze dependencies between the variables involved in arithmetic coding by means of the Bayesian formalism. This provides a suitable framework for designing a soft decoding algorithm that provides high error-resilience. It also provides a natural setting for "soft synchronization", i.e., to introduce anchors favoring the likelihood of "synchronized" paths. In order to maintain the complexity of the estimation within a realistic range, a simple, yet efficient, pruning method is described. The algorithm can be placed in an iterative source-channel decoding structure, in the spirit of serial turbo codes. Models and algorithms are then applied to context-based arithmetic coding widely used in practical systems (e.g., JPEG-2000). Experimentation results with both theoretical sources and with real images coded with JPEG-2000 reveal very good error resilience performances.

Coding theorems for turbo code ensembles

This paper is devoted to a Shannon-theoretic study of turbo codes. We prove that ensembles of parallel and serial turbo codes are "good" in the following sense. For a turbo code ensemble defined by a fixed set of component codes (subject only to mild necessary restrictions), there exists a positive number /spl gamma//sub 0/ such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than /spl gamma//sub 0/, the average maximum-likelihood (ML) decoder block error probability approaches zero, at least as fast as n/sup -/spl beta//, where /spl beta/ is the "interleaver gain" exponent defined by Benedetto et al. in 1996.

Joint source-channel turbo decoding of entropy-coded sources

We analyze the dependencies between the variables involved in the source and channel coding chain. This analysis is carried out in the framework of Bayesian networks, which provide both an intuitive representation for the global model of the coding chain and a way of deriving joint (soft) decoding algorithms. Three sources of dependencies are involved in the chain: (1) the source model, a Markov chain of symbols; (2) the source coder model, based on a variable length code (VLC), for example a Huffman code; and (3) the channel coder, based on a convolutional error correcting code. Joint decoding relying on the hidden Markov model (HMM) of the global coding chain is intractable, except in trivial cases. We advocate instead an iterative procedure inspired from serial turbo codes, in which the three models of the coding chain are used alternately. This idea of using separately each factor of a big product model inside an iterative procedure usually requires the presence of an interleaver between successive components. We show that only one interleaver is necessary here, placed between the source coder and the channel coder. The decoding scheme we propose can be viewed as a turbo algorithm using alternately the intersymbol correlation due to the Markov source and the redundancy introduced by the channel code. The intermediary element, the source coder model, is used as a translator of soft information from the bit clock to the symbol clock.

Iterative multiuser interference reduction: turbo CDMA

We view the asynchronous random code division multiple-access (CDMA) channel as a time-varying convolutional code. We study the case where the users encode their data, and, therefore, the single user transmitters and the CDMA channel appear as the concatenation of two coding systems. At the receiver we employ serial turbo decoding strategies. Unlike conventional turbo codes where both the inner and outer code may be selected, in our case, the inner code is due to the CDMA channel which we assume to be random. Nevertheless, the decoding system resembles the decoder of a serial turbo code and single-user performance is obtained even for numbers of users approaching the spreading code length.