Set Of Codewords Research Articles

Improved Bit Rate Control for Real-Time MPEG Watermarking

The alteration of compressed video bitstream due to embedding of digital watermark tends to produce unpredictable video bit rate variations which may in turn lead to video playback buffer overflow/underflow or transmission bandwidth violation problems. This paper presents a novel bit rate control technique for real-time MPEG watermarking applications. In our experiments, spread spectrum watermarks are embedded in the quantized DCT domain without requantization and motion reestimation to achieve fast watermarking. The proposed bit rate control scheme evaluates the combined bit lengths of a set of multiple watermarked VLC codewords, and successively replaces watermarked VLC codewords having the largest increase in bit length with their corresponding unmarked VLC codewords until a target bit length is achieved. The proposed method offers flexibility and scalability, which are neglected by similar works reported in the literature. Experimental results show that the proposed bit rate control scheme is effective in meeting the bit rate targets and capable of improving the watermark detection robustness for different video contents compressed at different bit rates.

Design of Embedded Self-Testing Checkers for t-UED and BUED Codes

In this article we present a new method for designing self-testing checkers for t-UED and BUED codes. The main idea of this method is to map words of the considered code to words of a code of the same type in which the value of t or the number of check bits is reduced and repeating this with the obtained words until a parity code is obtained, or to translate the code words into words of a code for which such a mapping is possible. First we consider Borden codes for t e 2k − 1, Bose, and Bose-Lin codes. The mapping operation is realized by averaging weights and check symbol values of the code words. The resulting checkers have a simple and regular structure. This structure is independent on the set of code words that is provided by the circuit under check. The checkers are very well suited for use as embedded checkers since they are self-testing with respect to single stuck-at faults under very weak assumptions. All three checker types can be tested with 2 or 3 code words. We also propose a novel approach to design checkers for Blaum codes that require much less code word tests than existing solutions.

Coding theory based models for protein translation initiation in prokaryotic organisms

Our research explores the feasibility of using communication theory, error control (EC) coding theory specifically, for quantitatively modeling the protein translation initiation mechanism. The messenger RNA (mRNA) of Escherichia coli K-12 is modeled as a noisy (errored), encoded signal and the ribosome as a minimum Hamming distance decoder, where the 16S ribosomal RNA (rRNA) serves as a template for generating a set of valid codewords (the codebook). We tested the E. coli based coding models on 5′ untranslated leader sequences of prokaryotic organisms of varying taxonomical relation to E. coli including: Salmonella typhimurium LT2, Bacillus subtilis, and Staphylococcus aureus Mu50. The model identified regions on the 5′ untranslated leader where the minimum Hamming distance values of translated mRNA sub-sequences and non-translated genomic sequences differ the most. These regions correspond to the Shine–Dalgarno domain and the non-random domain. Applying the EC coding-based models to B. subtilis, and S. aureus Mu50 yielded results similar to those for E. coli K-12. Contrary to our expectations, the behavior of S. typhimurium LT2, the more taxonomically related to E. coli, resembled that of the non-translated sequence group.

Soft-Decision Decoding of Fixed-Rate Entropy-Coded Trellis-Coded Quantizer Over a Noisy Channel

This paper presents new techniques to improve the performance of a fixed-rate entropy-coded trellis-coded quantizer (FE-TCQ) in transmission over a noisy channel. In this respect, we first present the optimal decoder for a fixed-rate entropy-coded vector quantizer (FEVQ). We show that the optimal decoder for the FEVQ can be a maximum likelihood decoder where a trellis structure is used to model the set of possible code words and the Viterbi algorithm is subsequently applied to select the most likely path through this trellis. In order to add quantization packing gain to the FEVQ, we take advantage of a trellis-coded quantization (TCQ) scheme. To prevent error propagation, it is necessary to use a block structure obtained through a truncation of the corresponding trellis. To perform this task in an efficient manner, we apply the idea of tail biting to the trellis structure of the underlying TCQ. It is shown that the use of a tail-biting trellis significantly reduces the required block length with respect to some other possible alternatives known for trellis truncation. This results in a smaller delay and also mitigates the effect of error propagation in signaling over a noisy channel. Finally, we present methods and numerical results for the combination of the proposed FEVQ soft decoder and a tail-biting TCQ. These results show that, by an appropriate design of the underlying components, one can obtain a substantial improvement in the overall performance of such a fixed-rate entropy-coded scheme.

Parallel error correcting codes

We introduce the concept of error codes, the error correcting codes for parallel channels. Here, a parallel channel is a set of channels such that the additive error over a finite field occurs in one of its members at time T if the same error occurs in all members at the same time. The set of codewords of a parallel error correcting code has to be a product set, if the messages transmitted are from independent information sources. We present a simple construction of optimal parallel error correcting codes based on ordinary optimal error correcting codes and a construction of optimal linear parallel codes for independent sources based on optimal ordinary linear error correcting codes. The decoding algorithms for these codes are provided as well.

A Maximum Likelihood Decoding Algorithm for Wireless Channels

A new maximum likelihood decoding (MLD) algorithm for linear block codes is proposed. The new algorithm uses the algebraic decoder in order to generate the set of candidate codewords. It uses the exact probability for each codeword as a new likelihood metric and a method to generate the appropriate set of codewords similar to Kaneko, et al., and Tanaka-Kakigahara algorithms. The performance of the proposed algorithm is the same as that of MLD as it is proved theoretically and verified by simulation results. The comparison with these similar algorithms shows that the new one always requires less average decoding complexity than those of the other algorithms. Finally, we compare the algorithms for terrestrial and satellite channels.

On unique, multiset, and set decipherability of three-word codes

The concepts of unique decipherability (UD), multiset decipherability (MSD), and set decipherability (SD) of codes were developed to handle some special problems in the transmission of information. In unique decipherability, different sequences of codewords carry different information. In multiset decipherability, the information of interest is the multiset of codewords used in the encoding process so that order in which transmitted words are received is immaterial. In set decipherability, it is the set of codewords that is relevant information so the order and the multiplicity of words are immaterial. Lempel (1986) showed that the UD and MSD properties coincide for two-word codes and conjectured that every three-word MSD code is a UD code. Guzman (1995) showed that the UD, MSD, and SD properties coincide for two-word codes and conjectured that these properties coincide for three-word codes. In this paper, we answer both conjectures positively for all three-word codes {C/sub 1/, C/sub 2/, C/sub 3/} satisfying |C/sub 1/|=|C/sub 2/|/spl les/|C/sub 3/|. Our procedures are based on techniques related to dominoes.

Linearly constrained generalized Lloyd algorithm for reduced codebook vector quantization

As linearly constrained vector quantization (LCVQ) is efficient for block-based compression of images that require low complexity decompression, it is a de facto standard for three-dimensional (3-D) graphics cards that use texture compression. Motivated by the lack of an efficient algorithm for designing LCVQ codebooks, the generalized Lloyd (1982) algorithm (GLA) for vector quantizer (VQ) codebook improvement and codebook design is extended to a new linearly constrained generalized Lloyd algorithm (LCGLA). This LCGLA improves VQ codebooks that are formed as linear combinations of a reduced set of base codewords. As such, it may find application wherever linearly constrained nearest neighbor (NN) techniques are used, that is, in a wide variety of signal compression and pattern recognition applications that require or assume distributions that are locally linearly constrained. In addition, several examples of linearly constrained codebooks that possess desirable properties such as good sphere packing, low-complexity implementation, fine resolution, and guaranteed convergence are presented. Fast NN search algorithms are discussed. A suggested initialization procedure halves iterations to convergence when, to reduce encoding complexity, the encoder considers the improvement of only a single codebook for each block. Experimental results for image compression show that LCGLA iterations significantly improve the PSNR of standard high-quality lossy 6:1 LCVQ compressed images.

On binary linear codes supporting t-designs

In this paper, we present classification results on self-orthogonal binary codes supporting designs, Therefore, we use special linear forms on the intersection numbers. In particular, one shows that a binary self-orthogonal code of distance d/spl les/18 whose set of minimal-weight codewords supports a 5-design has to be self-dual. We also prove that the codewords of any fixed weight in a [24m+22, 12m+11, 4m+6] Type I code support a 3-design.

CDMA codeword optimization: interference avoidance and convergence via class warfare

Interference avoidance has been shown to reduce total square correlation (TSC) for given ensembles of user signature waveforms (codewords) in a synchronous code-division multiple-access (CDMA) system. In all experiments we have conducted, sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords. Here we provide the first formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called warfare whereby users which reside in more heavily loaded areas of the signal space purposely interfere with (attack) the reception of users in less crowded areas. Coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary. Such attacks and subsequent codeword adjustment by attacked users are shown to strictly decrease TSC. Along the way we also show using linear algebra and a variant of stochastic ordering, equivalence between minimization of TSC and maximization of sum capacity.

Generation of a compact code for extended binary memoryless sources with low entropy

A method is proposed for configuring the compact code for extended binary memoryless sources with probabilistic deviations in symbol appearance. In an n-th order extended information source for binary memoryless sources, messages with identical appearance probabilities are generated abundantly. If these messages are grouped for treatment, no rearrangement of the messages encompassing the groups is generated in degenerate operations by the Huffman algorithm for low-entropy information sources where the appearance probability of the superior symbols approaches arbitrarily close to 1. That is the situation used in this paper. It is reported that the code length and sets of code words, average code length, and maximum code length of the compact code can be derived by a simple equation without forming a code tree. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(1): 70–77, 2000

Embedded Checker Architectures for Cyclic and Low-Cost Arithmetic Codes

Code checkers that monitor the outputs of a system can detect both permanent and transient faults. We present two novel architectures of embedded self-testing checkers for low-cost and cyclic arithmetic codes, one based on code word generators and adders, the other based on code word accumulators. In these schemes, the code checker receives all possible code words but one, irrespective of the number of different code words that are produced by the circuit under check (CUC). So any code checker can be employed that is self-testing for all or a particular subset of code words, and the structure of the code checker need not be tailored to the set of code words produced by the CUC. The proposed code word generators and accumulators are built from simple standard hardware structures, counters and end-around-carry adders. They can also be utilized in an off-line BIST environment as pattern generators and test response compactors.

Inverse Halftoning of Color Images Using Classified Vector Quantization

This paper extends and modifies classified vector quantization (CVQ) to solve the problem of inverse halftoning from error-diffused color images. The process consists of two phases: the encoding and decoding phases. The encoding process needs a codebook for the encoder which transforms a smoothed halftoned image to a set of codewords. The decoding process also requires a different codebook for the decoder which reconstructs a color image from a set of codewords. According the relationships between these two codebooks, we modified the traditional generalized Lloyd algorithm to fit our purpose. Using CVQ, the reconstructed color image can be stored in compressed form and no further compression may be required. This is different from the existing algorithms which reconstruct a monochrome image in an uncompressed form. The bit-rate is about 0.96 bits per pixel for encoding a reconstructed color image. As far as we know, this paper is the first of its kind to solve the inverse halftoning problem of color images.

Binary Tree Code Words as Context-Free Languages

Given a binary tree coding system, the set of valid code words of all binary trees can be considered as a context-free language over the alphabet used in the coding system. The complexity of the language obtained varies from one coding system to another. Xiang, Tang and Ushijima have recently proved some properties of such languages. We show that their results can be more easily proved by noticing the form of the generating grammar in question. Namely, in the simplest cases the language obtained is a left Szilard language, a very simple deterministic language. Moreover, we prove some new results concerning the 'binary tree languages'.

Embedded Parity and Two‐Rail TSC Checkers withError‐Memorizing Capability

In self‐checking systems, checkers usually do not receive all code words during normal operation. Missing code words may prevent a checker from achieving the totally self‐checking property. The paper presents a novel approach to the design of embedded parity and two‐rail checkers that allows a checker to receive all code words irrespective of the set of code words that is provided by the functional circuit. A checker gets all code words by an LFSR while at the same time it monitors the output of the functional circuit. Additionally, the LFSR is able to capture the error patterns of noncode words. Captured error patterns will be modified since they will cycle through the LFSR. Thus, noncode words that are not detected due to undetected checker faults can be detected in later instances of time. The proposed method can be extended to the design of checkers for linear codes.

An improvement of soft-decision maximum-likelihood decoding algorithm using hard-decision bounded-distance decoding

A new soft-decision maximum-likelihood decoding algorithm is proposed, which generates a set of candidate codewords using hard-decision bounded-distance decoding. By improving the generating method of input vectors for the bounded-distance decoding due to Kaneko et al. (see ibid., vol.40, no.3, p.320-27, 1994), the decoding time complexity is reduced without degradation of the performance. The space complexity is dependent on the bounded-distance decoding.

An Improved VQ Codebook Search Algorithm Using Principal Component Analysis

We present an improved codebook search algorithm in this paper. We call it thedouble test of principal components(DTPC). This algorithm speeds up the codebook search by searching only an appropriate sub-codebook instead of the whole set of codewords. Moreover, DTPC inherits several benefits from some previous techniques, such as the double test (DT) and the principal component analysis (PCA). Thus DTPC is much more efficient than the other algorithms. Simulation results confirm this efficiency. According to these results, the total number of the mathematical operations needed in DTPC is usually less than that needed in any other method, even if the MSE degradation of DTPC is limited within 0.13 dB. Furthermore, in some cases, this number of DTPC is only 3% of that in a full search.

On the concept of code-isomorphy

LetF be a finite set of cardinality ¦F¦ =q ≥2,n ≥ 1 an integer and ϱ:F n×Fn→ℕ0 theHamming metric. Acode isomorphism C → D between two block codesC,D $$ \subseteq$$ Fn is defined as an isometry which can be extended to an isometry of the whole space Fn. Any permutation π ∈S n of the positions canonically induces a so-calledequivalence map $$\tilde \pi$$ ∈ Aut Fn; any system κ ≔ (κ1,κ2,...,κn) ofn permutations of the character setF induces a so-calledconfiguration $$\tilde \kappa$$ ∈ Aat Fn. The group Aut Fn of all isometries of Fn turns out to be semidirect product of the configuration group with the symmetric group of degreen. The codeword estimating failure probability of a maximum likelihood codeword estimator for aq-nary symmetric channel does not depend on the transmitted codeword, if the automorphism group of the code acts transitively on the set of codewords. When using a systematic (n, k)-encoder, the symbol decoding failure probability does not depend on the transmitted symbol or on the time of transmission if the configuration group and the automorphism group act transitively on the set of codewords resp. on the set of thek information positions.

A directed search approach for unit-memory convolutional codes

A set of heuristic algorithms to numerically search for binary unit-memory convolutional codes (UMC) are presented along with a large number of new codes for 2/spl les/k/spl les/8 and code rate 1/4/spl les/R<1. Combinatorial optimization is used which involves selecting and then pairwise-matching column vectors of the two (n,k) UMC tap weight matrices. The column selection problem is that of finding the best (2n,k) binary, linear block code (BC). In this correspondence, the best BC generator matrix G is found by successively refining G using directed local exhaustive searches. In particular, the set of minimum-weight codewords are used to find a subset of G to exhaustively search. The UMC search strategy (pairwise matching problem) uses a directed local exhaustive search similar to the BC directed search by using the concept of the terminated BC of the UMC. The heuristic algorithms developed in this correspondence are very robust and converge relatively quickly to the optimal or near-optimal UMC. In addition, although it is generally possible to achieve the block code upper bound for free distance, we give a class of UMCs which cannot achieve this bound.

On the construction of maximal prefix-synchronized codes

We present a systematic procedure for mapping data sequences into codewords of a prefix-synchronized code (PS-code), as well as for performing the inverse mapping. A PS-code, proposed by Gilbert (1960), belongs to a subclass of comma-free codes and is useful to recover word synchronization when errors have occurred in the stream of codewords. A PS-code is defined as a set of codewords with the property that each codeword has a known sequence as a prefix, followed by a coded data sequence in which this prefix is not allowed to occur. The largest PS-code among all PS-codes of the same code length is called a maximal prefix-synchronized code (MPS-code). We develop an encoding and decoding algorithm for Gilbert's MPS-code with a prefix of the form 11...10 and extend the algorithm to the class PS-codes of which the prefix is self-uncorrelated. The computational complexity of the entire mapping process is proportional to the length of the codewords.