On Bounded Weight Codes

The maximum size of a binary code is studied as a function of its length N, minimum distance D, and minimum codeword weight W. This function B(N,D,W) is first characterized in terms of its exponential growth rate in the limit as N tends to infinity for fixed d=D/N and w=W/N. The exponential growth rate of B(N,D,W) is shown to be equal to the exponential growth rate of A(N,D) for w <= 1/2, and equal to the exponential growth rate of A(N,D,W) for 1/2< w <= 1. Second, analytic and numerical upper bounds on B(N,D,W) are derived using the semidefinite programming (SDP) method. These bounds yield a non-asymptotic improvement of the second Johnson bound and are tight for certain values of the parameters

NASA SERC 1990 Symposium on VLSI Design

This document contains papers presented at the first annual NASA Symposium on VLSI Design. NASA's involvement in this event demonstrates a need for research and development in high performance computing. High performance computing addresses problems faced by the scientific and industrial communities. High performance computing is needed in: (1) real-time manipulation of large data sets; (2) advanced systems control of spacecraft; (3) digital data transmission, error correction, and image compression; and (4) expert system control of spacecraft. Clearly, a valuable technology in meeting these needs is Very Large Scale Integration (VLSI). This conference addresses the following issues in VLSI design: (1) system architectures; (2) electronics; (3) algorithms; and (4) CAD tools

Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems

We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with oversampling factors of at least two, we provide prescriptions for the shortest filter length of the synthesis bank that would guarantee PR almost surely. The prescribed length is as short or shorter than the analysis filters and has an approximate inverse relationship with the oversampling factor. Our results are in form of necessary and sufficient statements that hold generically, hence only fail for elaborately-designed nongeneric examples. We provide extensive numerical verification of the theoretical results and demonstrate that the gap between the derived filter length prescriptions and the true minimum is small. The results have potential applications in synthesis FB design problems, where the analysis bank is given, and for analysis of fundamental limitations in blind signals reconstruction from data collected by unknown subsampled multi-channel systems.Comment: Manuscript submitted to IEEE Transactions on Signal Processin

TDRSS telecommunications system, PN code analysis

The pseudo noise (PN) codes required to support the TDRSS telecommunications services are analyzed and the impact of alternate coding techniques on the user transponder equipment, the TDRSS equipment, and all factors that contribute to the acquisition and performance of these telecommunication services is assessed. Possible alternatives to the currently proposed hybrid FH/direct sequence acquisition procedures are considered and compared relative to acquisition time, implementation complexity, operational reliability, and cost. The hybrid FH/direct sequence technique is analyzed and rejected in favor of a recommended approach which minimizes acquisition time and user transponder complexity while maximizing probability of acquisition and overall link reliability