Emanuele Viterbo

A universal lattice code decoder for fading channels

We present a maximum-likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver. The decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point. By judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment.

The golden code: a 2/spl times/2 full-rate space-time code with nonvanishing determinants

In this paper, the Golden code for a 2/spl times/2 multiple-input multiple-output (MIMO) system is presented. This is a full-rate 2/spl times/2 linear dispersion algebraic space-time code with unprecedented performance based on the Golden number 1+/spl radic/5/2.

The golden code: a 2 x 2 full-rate space-time code with non-vanishing determinants

In this paper we present the Golden code for a 2times2 MIMO system. This is a full-rate 2times2 linear dispersion algebraic space-time code with unprecedented performance based on the Golden number 1+radic5/2

Perfect Space–Time Block Codes

In this paper, we introduce the notion of perfect space-time block codes (STBCs). These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas

Good lattice constellations for both Rayleigh fading and Gaussian channels

Recent work on lattices matched to the Rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency. We present a new family of lattice constellations, based on complex algebraic number fields, which have good performance on Rayleigh fading channels. Some of these lattices also present a reasonable packing density and thus may be used at the same time over a Gaussian channel. Conversely, we show that particular versions of the best lattice packings (D/sub 4/, E/sub 6/, E/sub 8/, K/sub 12/, /spl Lambda//sub 16/, /spl Lambda//sub 24/), constructed from totally complex algebraic cyclotomic fields, present better performance over the Rayleigh fading channel. The practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links. Some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results.

On Fast-Decodable Space–Time Block Codes

We focus on full-rate, fast-decodable space-time block codes (STBCs) for 2 times 2 and 4times2 multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable 2times2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity 4times2 STBC, and show that it outperforms all previously known codes with certain constellations.

Algebraic number theory and code design for Rayleigh fading channels

Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems. Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit code constructions based on algebraic number theory are now available.The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory. The basic facts of this mathematical field will be illustrated by many examples and by the use of a computer algebra freeware in order to make it more accessible to a large audience.

Flip-OFDM for Unipolar Communication Systems

Unipolar communications systems can transmit information using only real and positive signals. This includes a variety of physical channels ranging from optical (fiber or free-space), to RF wireless using amplitude modulation with non-coherent reception, to baseband single wire communications. Unipolar OFDM techniques can efficiently compensate frequency selective channel distortion in unipolar communication systems. One of the leading example of unipolar OFDM is asymmetric clipped optical OFDM (ACO-OFDM) originally proposed for optical communications. Flip-OFDM is an alternative approach that was proposed in a patent, but its performance and full potentials have never been investigated in the literature. In this paper, we first compare Flip-OFDM and ACO-OFDM, and show that both techniques have the same performance but different complexities. In particular, Flip-OFDM offers 50% saving in hardware complexity at the receiver over ACO-OFDM. We then propose a new detection scheme, which enables to reduce the noise at the Flip-OFDM receiver by almost 3dB. The analytical performance of the noise filtering schemes is supported by the simulation results.

Cyclic Division Algebras: A Tool for Space-Time Coding

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space-Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes.

On Fast-Decodable Space-Time Block Codes

In this paper, we focus on full-rate, fast-decodable space-time block codes (STBCs) for 2 x 2 and 4 x 2 multiple-input multiple-output (MIMO) transmission. We first derive conditions for reduced-complexity maximum-likelihood decoding, and apply them to a unified analysis of two families of 2 x 2 STBCs that were recently proposed. In particular, we describe a reduced- complexity sphere decoding algorithm suitable for QAM signal constellations. Next, we derive a novel reduced-complexity 4 x 2 STBC, and show that it outperforms all previously known codes with certain constellations.