Generalized low-density codes with BCH constituents for full-diversity near-outage performance

A new graph-based construction of generalized low density codes (GLD-Tanner) with binary BCH constituents is described. The proposed family of GLD codes is optimal on block erasure channels and quasi-optimal on block fading channels. Optimality is considered in the outage probability sense. Aclassical GLD code for ergodic channels (e.g., the AWGN channel,the i.i.d. Rayleigh fading channel, and the i.i.d. binary erasure channel) is built by connecting bitnodes and subcode nodes via a unique random edge permutation. In the proposed construction of full-diversity GLD codes (referred to as root GLD), bitnodes are divided into 4 classes, subcodes are divided into 2 classes, and finally both sides of the Tanner graph are linked via 4 random edge permutations. The study focuses on non-ergodic channels with two states and can be easily extended to channels with 3 states or more.

Full diversity product codes for block erasure and block fading channels

We show how to build full-diversity product codes under both iterative encoding and decoding over non-ergodic channels, in presence of block erasure and block fading. The concept of a rootcheck or a root subcode is introduced by generalizing the same principle recently invented for low-density parity-check codes. We also describe some channel related graphical properties of the new family of product codes, a familyreferred to as root product codes.

A comparison of full-rate full-diversity 2x2 space-time codes for WiMAX systems

Multiple-input multiple-output (MIMO) techniques have become an essential part of broadband wireless communications systems. For example, the recently developed IEEE 802.16e specifications for broadband wireless access include three MIMOprofiles employing 2×2 space-time codes (STCs), and two of these MIMO schemes are mandatory on the downlink of Mobile WiMAX systems. One of these has full rate, and the other has full diversity, but neither of them has both of the desired features. The third profile, namely, Matrix C, which is not mandatory, is both a full rate and a full diversity code, but it has a high decoder complexity. Recently, the attention was turned to the decodercomplexity issue and including this in the design criteria, several full-rate STCs were proposed as alternatives to Matrix C. In this paper, we review these different alternatives and compare them to Matrix C in terms of performances and the correspondingreceiver complexities.

Outage thresholds of LDPC codes over nonergodic block-fading channels

This paper derives approximations allowing the estimation of outage probability for standard irregular LDPC codes and full-diversity Root-LDPC codes used over nonergodic block-fading channels. Two separate approaches are discussed: a numerical approximation, obtained by curve fitting, for both code ensembles, and an analytical approximation for Root-LDPC codes, obtained under the assumption that the slope of the iterative threshold curve of a given code ensemble matches the slope of the outage capacity curve in the high-SNR regime.

Parallel Research, Multiple Intellectual Property Right Protection Instruments, and the Correlation among R&D Projects, September 2005

The choice of a research path in attacking scientific and technological problems is a significant component of firms’ R&D strategy. One of the findings of the patent races literature is that, in a competitive market setting, firms’ noncooperative choices of research projects display an excessive degree of correlation, as compared to the socially optimal level. The paper revisits this question in a context in which firms have access to trade secrets, in addition to patents, to assert intellectual property rights (IPR) over their discoveries. We find that the availability of multiple IPR protection instruments can move the paths chosen by firms engaged in an R&D race toward the social optimum.

On iterative performance of LDPC and Root-LDPC codes over block-fading channels

This paper presents our investigation on iterativedecoding performances of some sparse-graph codes on block-fading Rayleigh channels. The considered code ensembles are standard LDPC codes and Root-LDPC codes, first proposed in and shown to be able to attain the full transmission diversity. We study the iterative threshold performance of those codes as a function of fading gains of the transmission channel and propose a numerical approximation of the iterative threshold versus fading gains, both both LDPC and Root-LDPC codes.Also, we show analytically that, in the case of 2 fading blocks,the iterative threshold root of Root-LDPC codes is proportional to (α1 α2)1, where α1 and α2 are corresponding fading gains.From this result, the full diversity property of Root-LDPC codes immediately follows.

Théâtre itinéraire de la Guerre actuelle entre les Turcs, d'une part, les Russes et les Impériaux, d'autre part : carte relative aussi au partage éventuel d'une partie de l'Empire Othoman / par M[onsieur Louis] Brion de la Tour, Ing[énieu]r Géographe du Roi

Échelle(s) : [1:3 400 000 ca] Échelle de Lieues d'une heure, ou de 20 au Degré 80 = [10,4 cm] (d'après échelles graphiques).

Théâtre itinéraire de la Guerre actuelle entre les Turcs, d'une part, les Russes et les Impériaux, d'autre part : carte relative aussi au partage éventuel d'une partie de l'Empire Othoman / par M[onsieur Louis] Brion de la Tour, Ing[énieu]r Géographe du Roi

Échelle(s) : [1:3 400 000 ca] Échelle de Lieues d'une heure, ou de 20 au Degré 80 = [10,4 cm] (d'après échelles graphiques).

Carte topographique de la route du Simplon entre Brieg et Domo d'Ossola / dressée par Ch[ar]les Picquet, géographe ord[inai]re du roi et de S.A.R m[onsei]g[neu]r le duc d'Orléans

Échelle(s) : 1:100 000

La Macedonia / descritta da Giacomo Cantelli da Vignola suddito, è Geografo del Serenis[si]mo Sig[no]r Duca di Modena ; Fran[cesc]us Donia Mess[anens]is sculp[si]t

Échelle(s) : [1:895 000 environ], Miglia Italiane 30 [= 6,1 cm]