On Non-Linear Finite State Digital Channel Coding

Abstract. A discrete-time digital channel coding, in which the encoder and decoder are both time-invariant finite state machines, is investigated. The channel is assumed to be memoryless. Two measures of performance are considered: the probability of error and the minimum free distance. Greater emphasis is placed on the minimum free distance since it is easier to evaluate than the probability of error criterion, and for small channel crossover probability it is a very good indicator of system performance; it is defined as the Hamming distance between two possible output sequences that correspond to distinct state sequences of the same length that are identical at both the start and finish. An algorithm to calculate the distance between such possible output sequences was developed; it also identifies all such pain of output sequence. Another algorithm, based on the finite state machine properties of the encoder, was found to generate the finite state decoder. Finally, after having found the pairs of encoder-decoder finite state machines, we simulated the communication system. Sari. Suatu kode saluran digital dengan waktu tercacah yang mempunyai pasangan encoder-decoder berupa mesin berkeadaan terhingga dan invarian waktu akan diteliti. Saluran dianggap tanpa daya ingat. Digunakan dua buah ukuran kinerja yaitu probabilitas kesalahan dan jarak bebas minimum. Penggunaan jarak bebas minimum lebih ditekankan karena lebih mudah dievaluasi dibandingkan probabilitas kesalahan. Untuk probabilitas kesalahan saluran yang kecil, jarak itu merupakan indikator yang sangat baik bagi kinerja sistem; ia didefinisikan sebagai jarak Hamming minimum antara dua buah kemungkinan sekuen keluaran yang berupa sekuen keadaan yang unik dengan panjang dan keadaan yang sama, baik di awal maupun di akhir sekuen. Sebuah algoritma untuk menghitung jarak antara sekuen keluaran yang sedemikian itu telah pula dikembangkan; algoritma tersebut juga mampu mengidentifikasi semua pasangan sekuen keluaran itu. Sebuah algoritma lainnya, didasarkan pada sifat-sifat encoder sebagai mesin dengan keadaan berhingga, yang mampu menyusun decoder dengan keadaan berhingga, telah pula ditemukan. Akhirnya, setelah menemukan berbagai pasangan encoder-decoder yang berupa mesin dengan keadaan berhingga, sistem komunikasi digital disimulasikan

Behavioral Learning of Aircraft Landing Sequencing Using a Society of Probabilistic Finite State Machines

Air Traffic Control (ATC) is a complex safety critical environment. A tower controller would be making many decisions in real-time to sequence aircraft. While some optimization tools exist to help the controller in some airports, even in these situations, the real sequence of the aircraft adopted by the controller is significantly different from the one proposed by the optimization algorithm. This is due to the very dynamic nature of the environment. The objective of this paper is to test the hypothesis that one can learn from the sequence adopted by the controller some strategies that can act as heuristics in decision support tools for aircraft sequencing. This aim is tested in this paper by attempting to learn sequences generated from a well-known sequencing method that is being used in the real world. The approach relies on a genetic algorithm (GA) to learn these sequences using a society Probabilistic Finite-state Machines (PFSMs). Each PFSM learns a different sub-space; thus, decomposing the learning problem into a group of agents that need to work together to learn the overall problem. Three sequence metrics (Levenshtein, Hamming and Position distances) are compared as the fitness functions in GA. As the results suggest, it is possible to learn the behavior of the algorithm/heuristic that generated the original sequence from very limited information

Designing structured tight frames via an alternating projection method

Tight frames, also known as general Welch-bound- equality sequences, generalize orthonormal systems. Numerous applications - including communications, coding, and sparse approximation- require finite-dimensional tight frames that possess additional structural properties. This paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems (IEPs), which includes the frame design problem. To apply this method, one needs only to solve a matrix nearness problem that arises naturally from the design specifications. Therefore, it is the fast and easy to develop versions of the algorithm that target new design problems. Alternating projection will often succeed even if algebraic constructions are unavailable. To demonstrate that alternating projection is an effective tool for frame design, the paper studies some important structural properties in detail. First, it addresses the most basic design problem: constructing tight frames with prescribed vector norms. Then, it discusses equiangular tight frames, which are natural dictionaries for sparse approximation. Finally, it examines tight frames whose individual vectors have low peak-to-average-power ratio (PAR), which is a valuable property for code-division multiple-access (CDMA) applications. Numerical experiments show that the proposed algorithm succeeds in each of these three cases. The appendices investigate the convergence properties of the algorithm

Perfect simulation of a coupling achieving the dˉ\bar{d}-distance between ordered pairs of binary chains of infinite order

We explicitly construct a coupling attaining Ornstein's $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of iid sequence of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.Comment: Typos corrected. The final publication is available at http://www.springerlink.co

Pushdown Compression

The pressing need for eficient compression schemes for XML documents has recently been focused on stack computation [6, 9], and in particular calls for a formulation of information-lossless stack or pushdown compressors that allows a formal analysis of their performance and a more ambitious use of the stack in XML compression, where so far it is mainly connected to parsing mechanisms. In this paper we introduce the model of pushdown compressor, based on pushdown transducers that compute a single injective function while keeping the widest generality regarding stack computation. The celebrated Lempel-Ziv algorithm LZ78 [10] was introduced as a general purpose compression algorithm that outperforms finite-state compressors on all sequences. We compare the performance of the Lempel-Ziv algorithm with that of the pushdown compressors, or compression algorithms that can be implemented with a pushdown transducer. This comparison is made without any a priori assumption on the data's source and considering the asymptotic compression ratio for infinite sequences. We prove that Lempel-Ziv is incomparable with pushdown compressors