Coded Modulation in C and MATLAB

This software, written separately in C and MATLAB as stand-alone packages with equivalent functionality, implements encoders and decoders for a set of nine error-correcting codes and modulators and demodulators for five modulation types. The software can be used as a single program to simulate the performance of such coded modulation. The error-correcting codes implemented are the nine accumulate repeat-4 jagged accumulate (AR4JA) low-density parity-check (LDPC) codes, which have been approved for international standardization by the Consultative Committee for Space Data Systems, and which are scheduled to fly on a series of NASA missions in the Constellation Program. The software implements the encoder and decoder functions, and contains compressed versions of generator and parity-check matrices used in these operations

Telemetry-Based Ranging

A telemetry-based ranging scheme was developed in which the downlink ranging signal is eliminated, and the range is computed directly from the downlink telemetry signal. This is the first Deep Space Network (DSN) ranging technology that does not require the spacecraft to transmit a separate ranging signal. By contrast, the evolutionary ranging techniques used over the years by NASA missions, including sequential ranging (transmission of a sequence of sinusoids) and PN-ranging (transmission of a pseudo-noise sequence) whether regenerative (spacecraft acquires, then regenerates and retransmits a noise-free ranging signal) or transparent (spacecraft feeds the noisy demodulated uplink ranging signal into the downlink phase modulator) relied on spacecraft power and bandwidth to transmit an explicit ranging signal. The state of the art in ranging is described in an emerging CCSDS (Consultative Committee for Space Data Systems) standard, in which a pseudo-noise (PN) sequence is transmitted from the ground to the spacecraft, acquired onboard, and the PN sequence is coherently retransmitted back to the ground, where a delay measurement is made between the uplink and downlink signals. In this work, the telemetry signal is aligned with the uplink PN code epoch. The ground station computes the delay between the uplink signal transmission and the received downlink telemetry. Such a computation is feasible because symbol synchronizability is already an integral part of the telemetry design. Under existing technology, the telemetry signal cannot be used for ranging because its arrival-time information is not coherent with any Earth reference signal. By introducing this coherence, and performing joint telemetry detection and arrival-time estimation on the ground, a high-rate telemetry signal can provide all the precision necessary for spacecraft ranging

A Generalization of Martin's Axiom

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the literature before.Comment: 36 page

Set Theory and its Place in the Foundations of Mathematics:a new look at an old question

This paper reviews the claims of several main-stream candidates to be the foundations of mathematics, including set theory. The review concludes that at this level of mathematical knowledge it would be very unreasonable to settle with any one of these foundations and that the only reasonable choice is a pluralist one

Set Theory and Structures

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure