Demodulation/Decoding of a DC Free Construction of the Gosset Lattice

Abstract

<p>Over the past decade, lattices have been increasingly recognized as an important source of codes for the Gaussian channel. The 8-dimensional Gosset lattice has figured prominently in these new developments because it offers an asymptotic coding gain of 3 dB over conventional pulse amplitude modulation and can be soft decision demodulated/decoded with a reasonable amount of speed. In the present work, we revive a little used definition of the Gosset lattice and show that codes derived from this construction exhibit a null at dc in their baseband spectrum. Such codes are useful as line codes for baseband signalling on channels that do not support a dc spectral component or for bandpass transmission where spectral shaping is required to combat intersymbol interference.</p> <p>Previous applications of lattice codes have been aimed primarily at voiceband data communications. This thesis was motivated by the need to develop a decoder that would make applications in the multi-megabit range of data transmission possible. To achieve this goal, a two-stage approach to demodulation was developed. The first stage makes a fast estimate of the transmitted vector and has the ability to declare an erasure when it knows its estimate is unreliable. This initial erasure declaring stage controls the throughput of the demodulator. Because it is far simpler than a maximum likelihood demodulator, greater speed is achieved. The second stage is provided to correct the occasional occurrence of an erasure and maintain the error performance of the lattice. To complete the decoder structure, we outline a method of lexicographic ordering the signal set that leads to a compact set of decoder look-up tables used to obtain a binary message sequence from each demodulated vector. Finally, we evaluate the effects of quantization on the probabilities of erasure and error and give results from a Monte-Carlo simulation undertaken to verify the demodulators performance.</p>