Showing papers by "Codex Corporation published in 1986"

A recursive modified Gram-Schmidt algorithm for least- squares estimation

Abstract: This paper presents a recursive form of the modified Gram-Schmidt algorithm (RMGS). This new recursive least-squares (RLS) estimation algorithm has a computational complexity similar to the conventional RLS algorithm, but is more robust to roundoff errors and has a highly modular structure, suitable for VLSI implementation. Its properties and features are discussed and compared to other LS estimation algorithms.

Numerically robust least-squares lattice-ladder algorithms with direct updating of the reflection coefficients

Abstract: New time-recursive equations are derived for the reflection coefficients and the ladder gains in the a priori and a posteriori forms of the exact least-squares (LS) lattice-ladder filtering algorithms. The numerical accuracy of the LS lattice-ladder algorithms obtained by use of these new direct time update equations is analyzed and compared to the accuracy resulting from the conventional LS lattice-ladder algorithms. The analysis and a number of simulation results which are presented lead us to conclude that the new a priori and a posteriori forms of the LS lattice-ladder algorithms yield superior performance.

Simplified decoding of lattices and codes

Abstract: A decoder including first and second decoding stages for selecting a codeword near to a given N-tuple r which is a sequence of N real values ri representing signals. The first stage includes substages associated respectively with sections rj of N-tuple r, each substage for evaluating distances between multiple sets of possible partial codewords and the section rj and for selecting a survivor from each of the multiple sets based on the distances. The second stage includes n-1 substages, each of which operates with respect to a supersection made up of a combination of two parts, each part being a section or a supersection combined in an earlier substage of the second stage and it includes a final substage which operates with respect to a final supersection whose parts make up the complete N-tuple r. Eachof the n-1 substages is for evaluating distances between multiple sets of possible partial codewords and the received values in the corresponding supersection based on the survivor distances for the survivors corresponding to each of the two parts and for selecting a survivor from each of the multiple sets based on the distances. The final substage is for evaluating distances between the codewords and the N-tuple r based on the survivor distances for the survivors corresponding to each of two parts, for selecting a finally decoded codeword based on the distances between the codewords and N-tuple r, and for providing information about the finally decoded codeword as decoder output.

Coded modulation system with a simplified decoder capable of reducing the effects of channel distortion

Abstract: A receiver for deciding which signal points were sent from a transmitter based on corresponding noise affected signals received via a distorting channel, the noise affected signals carrying information about a particular sequence of encoding states occupied in a succession of time intervals by a finite state process having a finite number of possible encoding states, the receiver including modifying circuitry for generating a plurality of different modified versions of each received signal, and a decoder for deciding which signal points were sent based on estimating a particular sequence of decoder states by storing a number of path histories of previous signal points and using the modified versions to extend the path histories, the different modified versions of each received signal numbering fewer than the number of stored path histories. In other aspects, the constellation of signal points is partitioned into decision subsets, each possible transitions from a possible decoder state are associated with a decision subset, based on the signal points in the path histories, and each of the modified versions is associated with one of the decision subsets; there are fewer modified versions than the number of decoder states; and the decoder states number fewer than the number of decoder states in an optimum trellis decoder.

Network collision detection and avoidance apparatus

Abstract: A technique for regulating the transmission of messages initiated simultaneously by a plurality of nodes of a network, in which clock intervals are established for the network, a sequence of digital values is included in each message and is transmitted to the medium at the rate of one digital value per clock interval, the sequences included in messages that are initiated at the same time by more than one node are transmitted in the same sequence of clock intervals, the presence on the medium of a selected digital value during any clock interval in which a node is transmitting a different digital value within the sequence of a message is detected, and the transmission of the message is interrupted by the node upon such detection, without corrupting another node's transmission.

A flexible, numerically robust array processing algorithm and its relationship to the givens transformation

Abstract: The development of systolic array processors is very important for real-time adaptive array processing applications. In this paper a numerically robust algorithm, based on the modified Gram-Schmidt (MGS) method, is presented. The algorithm can be efficiently realized using a systolic architecture and is capable of handling both exponential and finite memory windows in order to cope with time-varying data. Finally, the relation of these algorithms to similar schemes based on the Given's transformation is investigated.

Finite word-length effects in recursive least squares algorithms with application to adaptive equalization

Abstract: In this paper we provide a summary of recent and new results on finite word length effects in recursive least squares adaptive algorithms. We define the numerical accuracy and numerical stability of adaptive recursive least squares algorithms and show that these two properties are related to each other, but are not equivalent. The numerical stability of adaptive recursive least squares algorithms is analyzed theoretically and the numerical accuracy with finite word length is investigated by computer simulation. It is shown that the conventional recursive least squares algorithm gives poor numerical accuracy when a short word length is used. A new form of a recursive least squares lattice algorithm is presented which is more robust to round-off errors compared to the conventional form. Optimum scaling of recursive least squares algorithms for fixedpoint implementation is also considered.

Apparatus for transmitting streams of information bits and methods for estimating the most likely sequence sent

Abstract: Embodiments of apparatus are described for transmitting a stream of information bits by sending corresponding signals over a channel in a plurality of signalling slots. A family of multi-dimensional convolutionally coded modulation systems achieves enlarged minimum distance between possible sequences of signal points, reduced number of error events with the minimum distance, acceptable peak-to-average power ratio, reduced number of signal points in each constituent two-dimensional constellation, immunity to rapid carrier phase changes, and reduced complexity, resulting in a reduced error probability when maximum likelihood decoding is used. These advantages are achieved by the construction and by the partitioning into subsets of the multi- dimensional constellation, by the design of convolutional codes using those multi-dimensional subsets, by using a bit converter and a block encoder to convert a multi-dimensional constellation mapping into multiple two-dimensional constellation mappings, and by a simplified decoding technique.

A Custom VLSI Chip Set for Digital Signal Processing in High-Speed Voiceband Modems

Abstract: Systems modems intended for use in relatively large private networks are characterized by high performance, reliability and flexibility to support network management, and multiple modes of operation and user features. This paper describes a programmable digital signal processor which is teamed with a 16-bit microprocessor in a dual processor architecture satisfying the requirements of high-speed voiceband systems modems. The architecture of the two custom integrated circuits which form the basis of the signal processor is presented. This processor has novel arithmetic, data structure address generation, and program flow-control capabilities, which result in a high utilization of the arithmetic unit and a low program overhead for housekeeping tasks. Some of these features are illustrated by programming examples.

A family of pseudo-least squares estimation algorithms without division

Abstract: In this paper, we show that it is possible to approximate true division by dividing a number by a power-of-two in the LS lattice algorithm that is based on the new direct-coefficient-update form of the exact least squares (LS) lattice algorithm. The resulting pseudo-LS lattice algorithm is modestly slower in initial convergence than the true LS lattice algorithm, while it has a steady state error similar to the latter. The results are extended to a family of LS estimation algorithms covering a broader scope of applications.