Redundant Code Research Articles

Merging Fractal Image Compression and Wavelet Transform Methods

Fractal image compression and wavelet transform methods can be combined into a single compression scheme by using an iterated function system to generate the wavelet coefficients. The main advantage of this approach is to significantly reduce the tiling artifacts: operating in wavelet space allows range blocks to overlap without introducing redundant coding. Our scheme also permits reconstruction in a finite number of iterations and lets us relax convergence criteria. Moreover, wavelet coefficients provide a natural and efficient way to classify domain blocks in order to shorten compression times. Conventional fractal compression can be seen as a particular case of our general algorithm if we choose the Haar wavelet decomposition. On the other hand, our algorithm gradually reduces to conventional wavelet compression techniques as more and more range blocks fail to be properly approximated by rescaled domain blocks.

CETP and exchangeable apoproteins: common features in lipid binding activity.

In order to define the active domain for lipid binding in CETP (cholesteryl ester transfer protein), our study discusses some fundamental physicochemical properties of this molecule such as hydrophobic moment, protein active surface and helix amphipathicity, in comparison to the properties reported for a series of apoproteins including apoAI, apoAII, apoCI, CII, CIII and apoE. Our study suggests that CETP corresponds to a protein with an active surface slightly lower than the one calculated for the exchangeable apoproteins AI, AII, CI, CII, CIII and E. Arrays type (i, i + 3) and (i, i + 4) were found in the region associated to lipid binding in these apoproteins. Seven such arrays located in the amphipathic alpha-helices of CETP are also suggested to contribute to the overall lipid binding activity as a consequence of alpha-helix stability. It is proposed that for lipid binding to occur in both types of molecules, the possibility of a conformational specificity given by a redundant stereochemical code can be actively operating.

On the implementation of minimum redundancy prefix codes

Minimum redundancy coding (also known as Huffman coding) is one of the enduring techniques of data compression. Many efforts have been made to improve the efficiency of minimum redundancy coding, the majority based on the use of improved representations for explicit Huffman trees. In this paper, we examine how minimum redundancy coding can be implemented efficiently by divorcing coding from a code tree, with emphasis on the situation when n is large, perhaps on the order of 10/sup 6/. We review techniques for devising minimum redundancy codes, and consider in detail how encoding and decoding should be accomplished. In particular, we describe a modified decoding method that allows improved decoding speed, requiring just a few machine operations per output symbol (rather than for each decoded bit), and uses just a few hundred bytes of memory above and beyond the space required to store an enumeration of the source alphabet.

Modeling the complexity of genetic networks: Understanding multigenic and pleiotropic regulation

AbstractMolecular genetics presents an increasingly complex picture of the genome and biological function. Evidence is mounting for distributed function, redundancy, and combinatorial coding in the regulation of genes. Satisfactory explanation will require the concept of a parallel processing signaling network. Here we provide an introduction to Boolean networks and their relevance to present‐day experimental research. Boolean network models exhibit global complex behavior, self‐organization, stability, redundancy and periodicity, properties that deeply characterize biological systems. While the life sciences must inevitably face the issue of complexity, we may well look to cybernetics for a modeling language such as Boolean networks which can manageably describe parallel processing biological systems and provide a framework for the growing accumulation of data. We finally discuss experimental strategies and database systems that will enable mapping of genetic networks. The synthesis of these approaches holds an immense potential for new discoveries on the intimate nature of genetic networks, bringing us closer to an understanding of complex molecular physiological processes like brain development, and intractable medical problems of immediate importance, such as neurodegenerative disorders, cancer, and a variety of genetic diseases.

Bounded distance+1 soft-decision Reed-Solomon decoding

We present a new Reed-Solomon decoding algorithm, which embodies several refinements of an earlier algorithm. Some portions of this new decoding algorithm operate on symbols of length lgq bits; other portions operate on somewhat longer symbols. In the worst case, the total number of calculations required by the new decoding algorithm is proportional to nr, where n is the code's block length and r is its redundancy. This worst case workload is very similar to prior algorithms. But in many applications, average-case workload and error-correcting performance are both much better. The input to the new algorithm consists of n received symbols from GF(q), and n nonnegative real numbers, each of which is the reliability of the corresponding received symbol. Any conceivable errata pattern has a "score" equal to the sum of the reliabilities of its locations with nonzero errata values. A max-likelihood decoder would find the minimum score over all possible errata patterns. Our new decoding algorithm finds the minimum score only over a subset of these possible errata patterns. The errata within any candidate errata pattern may be partitioned into "errors" and "erasures," depending on whether the corresponding reliabilities are above or below an "erasure threshold." Different candidate errata patterns may have different thresholds, each chosen to minimize its corresponding ERRATA COUNT, which is defined as 2/spl middot/(number of errors)+(number of erasures). The new algorithm finds an errata pattern with minimum score among all errata patterns for which ERRATA COUNT/spl les/r+1 where r is the redundancy of the RS code. Conventional algorithms also require that the erasure threshold be set a priori; the new algorithm obtains the best answer over all possible settings of the erasure threshold. Conventional cyclic RS codes have length n=q-1, and their locations correspond to the nonzero elements of GF(q). The new algorithm also applies very naturally to RS codes which have been doubly extended by the inclusion of 0 and /spl infin/ as additional locations.

Parallelization of Control Recurrences for ILP Processors

The performance of applications executing on processors with instruction level parallelism is often limited by control and data dependences. Performance bottlenecks caused by dependences can frequently be eliminated through transformations which reduce the height of critical paths through the program. The utility of these techniques can be demonstrated in an increasingly broad range of important situations. This paper focuses on the height reduction of control recurrences within loops with data dependent exits. Loops with exits are transformed so as to alleviate performance bottlenecks resulting from control dependences. A compilation approach to effect these transformations is described. The techniques presented in this paper used in combination with prior work on reducing the height of data dependences provide a comprehensive approach to accelerating loops with conditional exits. In many cases, loops with conditional exits provide a degree of parallelism traditionally associated with vectorization. Multiple iterations of a loop can be retired in a single cycle on a processor with adequate instruction level parallelism with no cost in code redundancy. In more difficult cases, height reduction requires redundant computation or may not be feasible.

Redundancy rates for renewal and other processes

Upper and lower bounds, both of order /spl radic/n, are obtained on minimax redundancy of universal lossless codes for the class of renewal processes. This is the first example of an interesting model class with strong redundancy rate o(n) but not O(log n). For the same class, the nonexistence of weak-rate bounds of smaller order than /spl radic/n is also shown. The methods extend to provide upper and lower redundancy rate bounds of order n/sup (k+1)//(k+2) for the class of processes that are Markov renewal of order k. The weak-rate methods also extend to show the nonexistence of o(n) weak-rate bounds for the class of regenerative processes.

Hierarchical universal coding

In an earlier paper, we proved a strong version of the redundancy-capacity converse theorem of universal coding, stating that for most sources in a given class, the universal coding redundancy is essentially lower-bounded by the capacity of the channel induced by this class. Since this result holds for general classes of sources, it extends Rissanen's (1986) strong converse theorem for parametric families. While our earlier result has established strong optimality only for mixture codes weighted by the capacity-achieving prior, our first result herein extends this finding to a general prior. For some cases our technique also leads to a simplified proof of the above mentioned strong converse theorem. The major interest in this paper, however, is in extending the theory of universal coding to hierarchical structures of classes, where each class may have a different capacity. In this setting, one wishes to incur redundancy essentially as small as that corresponding to the active class, and not the union of classes. Our main result is that the redundancy of a code based on a two-stage mixture (first, within each class, and then over the classes), is no worse than that of any other code for most sources of most classes. If, in addition, the classes can be efficiently distinguished by a certain decision rule, then the best attainable redundancy is given explicitly by the capacity of the active class plus the normalized negative logarithm of the prior probability assigned to this class. These results suggest some interesting guidelines as for the choice of the prior. We also discuss some examples with a natural hierarchical partition into classes.

Condition handling in SQL persistent stored modules

The national and international standards committees responsible for Database Language SQL have proposed a candidate extension for SQL Persistent Stored Modules (SQL/PSM). The purpose of this extension is to provide a computationally complete language for the declaration and invocation of SQL stored modules and routines. Typically, such routines are stored in a database Server and executed from an application Client in a Client/Server environment.The proposed SQL/PSM consists of syntax and semantics for variable and cursor declarations, function and procedure (routines) invocations, condition handling, and control statements for looping and branching. An SQL routine is block structured, with each block consisting of local variable and condition handler declarations, a list of SQL statements, and local condition handler execution.Condition handling is a major new feature of SQL/PSM (henceforth referred to as PSM), although the style and comprehensiveness of the specification is still an issue in further progression of the standard. The specification currently under ballot includes conditions for exceptions, warnings, and other completions such as success of no data, and handlers for Continue, Exit, Redo, and Undo.Condition handling allows the user to separate condition handling code from the main flow of a routine, thereby eliminating the need to write numerous short and redundant code fragments to handle each unique condition. In some database products, one cannot even resolve the condition in the Server and must instead resort to the Client application program for resolution. Such approaches are often tedious, error-prone, and inflexible. Condition handling in the SQL module avoids these expensive alternatives, instead allowing the procedure to resolve its own conditions and then resume processing.Condition handling allows one to centralize the handling of conditions and gives users control over two major areas: run-time recovery from failures, and effects of conditions on transactions.Run-time recovery from failures has the following characteristics:• allows a user to handle any run-time condition, either by exiting gracefully or by attempting recovery• provides a recovery mechanism that includes the ability to resolve a condition and then resume action at the statement that caused the condition to be raised (if it was resolved)• provides the ability to define what "code" will handle each conditionAfter a condition has been resolved, what is the state of the transaction? Condition handling must ensure that the SQL-data, schemas, and SQL-variables are all maintained in an appropriate stable state and can be committed or rolled back. Additionally, the transaction must comply with the ACID test rules.Thus, the benefits of condition handling include:• allows reduction of error recovery code• creates a model for trapping and resolving conditions• provides the ability to resolve the condition and if possible to continue on• avoids the cost of requiring the SQL-client to resolve the condition• provides for greater data and path consistency in handling conditions• separates one condition from another

The mutational demography of protein C deficiency

The geographical distribution and prevalence of 256 single base-pair substitutions (105 of them being different) within the coding region of the human protein C (PROC) gene were correlated with their initial likelihoods of generation. A significant positive correlation was observed between these "mutational likelihoods" and the geographical dispersal of the PROC gene lesions within and between 16 different countries. This relationship could be attributed to the fact that, with few exceptions, high dispersal was only exhibited by CG-->TG and CG-->CA transitions, i.e. those substitutions that are known to arise de novo at the highest frequency. The statistical distribution of mutational likelihoods was as predicted on the basis of the PROC cDNA sequence alone, allowing however for the redundancy of the genetic code. These findings suggest (1) that genetic drift and lesion-specific selection have been of relatively minor importance in determining the mutational spectrum observed in the PROC gene and (2) that most multiple reports of particular substitutions in different geographical locations appear to reflect recurrent mutation rather than identity-by-descent.

Subword complexity of a generalized Thue-Morse word

Abstract Let y = y(0)y(1)y(2) … be an infinite word over a finite alphabet, and let py(r) count the number of distinct subwords of y of length r. In this paper we determine py(r) when y(i) = s2(i) mod k, where s2(i) denotes the sum of the base-2 digits of i. Our method is based on determining the redundancy of a certain code for subwords of a related infinite word.

Fault tolerant arithmetic unit using duplication and residue codes

This paper is a study of the practical value of the various approaches, proposed so far, to achieve fault tolerance in arithmetic units using the residue code technique and to find the best design in terms of cost and error coverage. The results have shown that the error correction approaches can treat a one-bit error ( E = ± 2 i ) using relatively small hardware cost and time delay. It is also shown that no more than a single error, of the one-bit type, can be treated at reasonable cost using error correction approaches. However, a combination of N-modular redundancy (NMR) and residue codes can be used to cover a wide range of errors at considerably lower cost. Here we suggest anapproach based on model duplication and residue codes (DAR) which is shown to have better error coverage than error correction approaches and lower cost than both triple modular redundancy (TMR) and error correction approaches.

Interprocedural partial redundancy elimination and its application to distributed memory compilation

Partial Redundancy Elimination (PRE) is a general scheme for suppressing partial redundancies which encompasses traditional optimizations like loop invariant code motion and redundant code elimination. In this paper we address the problem of performing this optimization interprocedurally. We use interprocedural partial redundancy elimination for placement of communication and communication preprocessing statements while compiling for distributed memory parallel machines.

The power of assignment motion

Assignment motion (AM) and expression motion (EM) are the basis of powerful and at the first sight incomparable techniques for removing partially redundant code from a program. Whereas AM aims at the elimination of complete assignments, a transformation which is always desirable, the more flexible EM requires temporaries to remove partial redundancies. Based on the observation that a simple program transformation enhances AM to subsume EM, we develop an algorithm that for the first time captures all second order effects between AM and EM transformations. Under usual structural restrictions, the worst case time complexity of our algorithm is essentially quadratic, a fact which explains the promising experience with our implementation.

A strong version of the redundancy-capacity theorem of universal coding

The capacity of the channel induced by a given class of sources is well known to be an attainable lower bound on the redundancy of universal codes with respect to this class, both in the minimax sense and in the Bayesian (maximin) sense. We show that this capacity is essentially a lower bound also in a stronger sense, that is, for most sources in the class. This result extends Rissanen's (1984, 1986) lower bound for parametric families. We demonstrate the applicability of this result in several examples, e.g., parametric families with growing dimensionality, piecewise-fixed sources, arbitrarily varying sources, and noisy samples of learnable functions. Finally, we discuss implications of our results to statistical inference. >

Learning Population Codes by Minimizing Description Length

The minimum description length (MDL) principle can be used to train the hidden units of a neural network to extract a representation that is cheap to describe but nonetheless allows the input to be reconstructed accurately. We show how MDL can be used to develop highly redundant population codes. Each hidden unit has a location in a low-dimensional implicit space. If the hidden unit activities form a bump of a standard shape in this space, they can be cheaply encoded by the center of this bump. So the weights from the input units to the hidden units in an autoencoder are trained to make the activities form a standard bump. The coordinates of the hidden units in the implicit space are also learned, thus allowing flexibility, as the network develops a discontinuous topography when presented with different input classes.

Correcting a specified set of likely error patterns

The main concern of this article is to find linear codes which will correct a set of arbitrary error patterns. Although linear codes which have been designed for correcting random error patterns and burst error patterns can be used, we would like to find codes which will correct a specified set of error patterns with the fewest possible redundant bits. Here, to reduce the complexity involved in finding the code with the smallest redundancy which can correct a specified set of error patterns, algebraic codes whose parity check matrix exhibits a particular structure are considered. If the number of redundant bits is T, the columns of the parity check matrix must be increasing powers of a field element in GF(2/sup T/). Given a set of error patterns to be corrected, computations to determine the code rates possible for these type of codes and hence the redundancy for different codeword lengths are presented. Results for various sets of error patterns suggest that the redundancy of these algebraic codes is close to the minimum redundancy possible for the set of error patterns specified and for any codeword length. >

On computing undetected error probabilities on the Gilbert channel

Two methods for computing the probability of undetected error on the Gilbert (1960) channel are examined. First, using a method proposed by Kittel (1978), we study some standard cyclic redundancy codes and compare the results with those on the binary symmetric channel. Then we consider a general method of approximate code evaluation, proposed by Elliott, which involves P(m, n), the probability of m errors in a block of length n bits. A nonrecursive technique for computing P(m, n) on the Gilbert channel is described.

The Origin and Evolution of the Genetic Code

We argue that a primitive genetic code with only 20 separate words explains that there are 20 coded amino acids in modern life. The existence of 64 words on the modern genetic code requires modern life to read almost exclusively one strand of DNA in one direction. In our primitive code, both the original and the complementary sequence are read in either direction to give the same strings of amino acids. The algebra of complements forces synonymy of primitive codons so as to reduce the 64 independent codons of the modern code to exactly 20 independent separate words in the primitive condition. The synonymy in the modern code is the result of selection rather than algebraic forcing. The primitive code has almost no resilience to base mutations, unlike the third base redundancy of the modern code. Our primitive and the modern code are orthogonal. If palindromic proteins were coded by hairpin DNA or RNA, then (i) no punctuation would be needed; (ii) the reverse reading would give the same secondarily folded protein structure; and (iii) the sugar backbone would be read in the conventional 5′ to 3′ direction for the original arm and its complement. Modern copying of genetic material is almost always antiparallel. However, occasional parallel copying, as does occur in modern life, would give the complementary hairpin that would also read 5′ to 3′ along its entire length. The parallel copy would reverse the direction of the order of bases with respect to the sugar backbone, and so it would be read in reverse order of bases, but by normal ribosomal processes. Our argument studiously avoids plausible anecdotes, an endemic flaw of evolutionary discussions.

Visual image processing by neural networks with nonlocal coupling

The possibilities of using homogeneous artificial neural networks both for encoding and back reconstruction of visual images are investigated. A conjugate reverse neural network with an opposite time direction is used for the image reconstruction. Information-entropic characteristics of the image and its different-level histograms are used for quality monitoring of the dynamic image processing. Experimental data on the dynamic behavior of these values in computer simulation for pure images are reported. Comparison with the thermodynamic entropy, subject to a monotonic change, is made. Special cases of nonmonotonic entropy change are considered and examples of the dynamic processing of images with code redundancy are demonstrated.