Priti Shankar

On BCH codes over arbitrary integer tings (Corresp.)

Bose-Chadhuri-Hocquenghem (BCH) codes with symbols from an arbitrary finite integer ring are derived in terms of their generator polynomials. Tile derivation is based on the factorization of x^{n}-1 over the unit ring of an appropriate extension of the Finite integer ring. The construction is thus shown to be similar to that for BCH codes over finite fields.

Computing the Stopping Distance of a Tanner Graph Is NP-Hard

Two decision problems related to the computation f stopping sets in Tanner graphs are shown to be NP-complete. It follows as a consequence that there exists no polynomial time algorithm for computing the stopping distance of a Tanner graph unless P = NP.

A simple and fast scheme for code compression for VLIW processors

Summary form only given. A scheme for code compression that has a fast decompression algorithm, which can be implemented using simple hardware, is proposed. The effectiveness of the scheme on the TMS320C62x architecture that includes the overheads of a line address table (LAT) is evaluated and obtained compression rates ranging from 70% to 80%. Two schemes for decompression are proposed. The basic idea underlying the scheme is a simple clustering algorithm that partially maps a block of instructions into a set of clusters. The clustering algorithm is a greedy algorithm based on the frequency of occurrence of various instructions.

On viewing block codes as finite automata

Block codes are viewed from a formal language theoretic perspective. It is shown that properties of trellises for subclasses of block codes called rectangular codes follow naturally from the Myhill Nerode theorem. A technique termed subtrellis overlaying is introduced with the object of reducing decoder complexity. Necessary and sufficient conditions for trellis overlaying are derived from the representation of the block code as a group, partitioned into a subgroup and its cosets. The conditions turn out to be simple constraints on coset leaders. It is seen that overlayed trellises are tail-biting trellises for which decoding is generally more efficient than that for conventional trellises. Finally, a decoding algorithm for tail-biting trellises is described, and the results of some simulations are presented.

Compressing XML documents using recursive finite state automata

We propose a scheme for automatically generating compressors for XML documents from Document Type Definition(DTD) specifications. Our algorithm is a lossless adaptive algorithm where the model used for compression and decompression is generated automatically from the DTD, and is used in conjunction with an arithmetic compressor to produce a compressed version of the document. The structure of the model mirrors the syntactic specification of the document. Our compression scheme is on-line, that is, it can compress the document as it is being read. We have implemented the compressor generator, and provide the results of experiments on some large XML databases whose DTDs are specified. We note that the average compression is better than that of XMLPPM, the only other on-line tool we are aware of. The tool is able to compress massive documents where XMLPPM failed to work as it ran out of memory. We believe the main appeal of this technique is the fact that the underlying model is so simple and yet so effective.

A simple algorithm for partial redundancy elimination

Partial redundancy elimination was originally formulated as a bidirectional, bit-vector, data-flow analysis problem by Morel and Renvoise. Dhamdhere improved the original algorithm using the concept of edge placement. Knoop, Rüthing, and Steffen viewed the problem within a framework that required only four unidirectional analyses for an optimal solution. Here, we propose an algorithm for partial redundancy elimination based on well known concepts, viz., availability, anticipability, partial availability, and partial anticipability. The algorithm is both computationally and lifetime optimal. Our algorithm also requires four unidirectional data-flow analyses. The main advantage of the algorithm is its simplicity.

Unifying Views of Tail-Biting Trellis Constructions for Linear Block Codes

In this paper, we present new ways of describing and constructing linear tail-biting trellises for block codes. We extend the well-known Bahl-Cocke-Jelinek-Raviv (BCJR) construction for conventional trellises to tail-biting trellises. The BCJR-like labeling scheme yields a simple specification for the tail-biting trellis for the dual code, with the dual trellis having the same state-complexity profile as that of the primal code . Finally, we show that the algebraic specification of Forney for state spaces of conventional trellises has a natural extension to tail-biting trellises

A new algorithm for linear regular tree pattern matching

We consider the problem of linear regular tree pattern matching and describe a new solution based on a bottom up technique. Current bottom up techniques preprocess the patterns and construct a finite state tree pattern matching automaton for the purpose. Though matching time is linear in the size of the subject tree, the size of the automaton can be exponential in the sum of the sizes of all patterns. We show here that the problem can be cast as a parsing problem for a context free language, and a solution that uses an extension of the LR parsing technique can be devised. Though the size of the resulting pushdown automaton can be exponential in the pattern size in the worst case, there are problem instances for which exponential gains in succinctness of representation are obtained. The technique has been successfully applied to the problem of generation of an instruction selector in a compiler back end.

Partial redundancy elimination: a simple, pragmatic, and provably correct algorithm

We propose a new algorithm for partial redundancy elimination based on the new concepts of safe partial availability and safe partial anticipability. These new concepts are derived by the integration of the notion of safety into the definitions of partial availability and partial anticipability. The algorithm works on flow graphs whose nodes are basic blocks. It is both computationally and lifetime optimal and requires four unidirectional analyses. The most important feature of the algorithm is its simplicity; the algorithm evolves naturally from the new concept of safe partial availability.

Threaded linear hierarchical quadtrees for computation of geometric properties of binary images

A modification of the linear quadtree, the threaded linear hierarchical quadtree (TLHQT), is proposed for the computation of geometric properties of binary images. Since most of the algorithms used in connection with computation of geometric properties require frequent exploration of adjacencies, a structure that keeps permanently in memory some adjacency links is introduced. Some results obtained by using the TLHQT for labeling connected components and for evaluating the perimeter and Eulers number in a quadtree environment are presented. The performance of the TLHQT is discussed. >