CHANNEL CODING PAGE

The CHANNEL CODING PAGE

This page is dedicated to error-correcting codes and their applications in digital communications and information theory. Thank you for visiting this page. For any comment or information regarding this page, please contact me at boutros at tamu dot edu. Last modification made on Spring 2018.

Joseph Jean Boutros

PERFORMANCE COMPARISON OF SHORT-LENGTH ERROR-CORRECTING CODES

We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. BCH, Reed-Muller, LDPC, and Polar codes are considered.

Click To Enter

CIRCULAR QAM CONSTELLATIONS

Circular Quadrature Amplitude Modulations (CQAM) were discovered in a recent work. The paper was published at the 2017 IEEE International Symposium on Information Theory (ISIT) and can be downloaded here.

In this web page, we give some extra properties of CQAM and extra nice drawings of CQAM constellations we could not include in the conference paper at ISIT’2017.

Click To Enter

The content below dates back to 2008, it is under renovation.

I will do my best to update asap. Joseph

GLD CODES

GLD Codes

This is the 10^th anniversary of GLD codes!

GLD stands for Generalized Low Density. These codes are Tanner structures with pseudo-random permutations. Under the impulse of Gilles Zémor, I started to study those codes in 1997 with Olivier Pothier. The first document on GLD codes dates back to January 1998. It has been submitted to ITW’1998. For some reason, we have been told 4 months later that the organizers cannot accept its publication due to the lack of space at the workshop…The work appeared later at ICC’99 and VTC’99. More recently, we developped full-diversity GLD codes for wireless channels with slow fading, i.e., quasi-static fading channels referred to as non-ergodic or block-fading channels.

Click To Enter

This directory has been updated on January 12, 2008.

Two simple exercises on point lattices A₂ and E₈

I- Sphere Decoder

II- Complex Construction for E₈

Download in PS

Download in PDF

Last update on June 2006.

For Graduate and Undergraduate Students

3 Exams in Wireless Communications Theory

I- Fading in Wireless Channels. PS. PDF.

II- Coding for Wireless Channels. PS. PDF.

III- Multiuser Detection and Rake Receiver in CDMA. PS. PDF.

Description: j0232136

Last update on November 2008.

AUTHORS	TITLE	My Comments	Download Format and Size
Robert G. Gallager	Low-density parity-check codes, MIT, 1963	Ph.D. report by Robert Gallager. LDPC codes first published by the author in 1962 are the ancestors of Turbo codes.	PDF (640K) , PS (1.0M) , PS+GZ (258K)
Emanuele Viterbo & Ezio Biglieri	A universal decoding algorithm for lattice codes, September 1993	Paper published at GRETSI’1993 in Juan-Les-Pins, France. Emanuele was the first to introduce the universal lattice decoder in the IEEE community. I called it Sphere Decoder while we were developping the C program in my software library in 1994.	PDF (1.5M)
Joseph J. Boutros	Lattice codes for Rayleigh fading channels. Réseaux de points pour les canaux à évanouissements, June 1996.	Ph.D. report, ENST Paris, France. Directed by Jean-Claude Belfiore. The sphere decoding alorigthm is in chapter 3, an introduction to algebraic number theory and rotated modulations for fading channels. This was a direct extension of Boutros thesis (mémoire de fin d’études ENST) on algebraic construction of lattices in 1992.	PDF (1.5M) , PS (1.3M) , PS+GZ (349K)
Emanuele Viterbo	Analysis of lattice constellations.Tecniche matematiche computazionali per l’analisi ed il progetto di costellazioni a reticolo, Februray 1995.	Ph.D. report, Politecnico di Torino, Italy. Directed by Ezio Biglieri. Our joint work on rotated lattices from algebraic number theory and rotated QAM modulations can be found in both PhD reports. Emanuele’s report includes also the Diamond cutting algorithm for Voronoi cells.	PDF (3.3M) , PS (3.4M) , PS+GZ (774K)
Emanuele Viterbo & Joseph Boutros	A universal lattice code decoder for fading channels, June 1999 (submitted to the IT Transactions in 1996!)	The sphere decoder paper for fading channels published in the IEEE Information Theory Transactions. Nowadays, the sphere decoder is applied in MIMO, OFDM and CDMA systems.	PDF (122K)
Loïc Brunel	Channel decoding algorithms for code division multiple access. Algorithmes de décodage de canal pour l’accès multiple à étalement de spectre, December 1999.	Ph.D. report, ENST Paris, France. Directed by Joseph Boutros. You can find here how to do multiple access without PN spreading (Turbo CDMA) and how to use the sphere decoder in CDMA. The first part is a nice introduction to multiuser-detection in DS-CDMA (in french). Density evolution results on the performance of some detectors are also included in this document.	PDF (2.3M) , PS (2.8M) , PS+GZ (708K)
Olivier Pothier	Compound codes based on graphs and their iterative decoding. Codes composites construits à partir de graphes et leur décodage itératif, January 2000.	Ph.D. report, ENST Paris, France. Directed by Joseph Boutros. You find here extensive details and results on Turbo codes, the convergence of iterative APP decoding, Generalized Low Density codes (GLD/Tanner) in both matrix and graph representations, and the design of interleavers for such codes on graphs. This Ph.D. document is written in english.	PDF (2.1M) , PS (3.3M) , PS+GZ (710K)
Catherine Lamy	High spectral efficiency communications over the Rayleigh fading channel. Communications à grande efficacité spectrale sur le canal à évanouissements, April 2000.	PhD report, ENST Paris, France. Directed by Joseph Boutros. Plenty stuff on algebraic and non-algebraic multi-dimensional rotations, Fast rotation transform (FRT), ML and DFE-MSE decoding of lattices, bit-interleaved coded modulation (BICM) and EM channel estimation for multiple antenna channels. You also find a capacity analysis of rotated modulations on a fading channel. This document is written in french.	PDF (1.3M) , PS (3.1M) , PS+GZ (768K)
Sandrine Vialle	Construction and analysis of new efficient channel coding structures for iterative decoding. Construction et analyse de nouvelles structures de codage de canal adaptées au décodage itératif, December 2000.	Ph.D. report, ENST Paris, France. Directed by Joseph Boutros. You find in this document the performance limits of finite length optimal codes under ML decoding, the definition and analysis of GLD (Tanner) codes based on convolutional codes and extensive results on Density Evolution thresholds for many channel coding families. This document is written in french.	PDF (3.3M) , PS (3.3M) , PS+GZ (788K)
Céline Durand	High spectral efficiency modulations for non coherent transmissions. Modulations à haute efficacité spectrale pour les transmissions non cohérentes, December 2000.	Ph.D. report, ENST Paris, France. Directed by Joseph Boutros. You find correlated multi-dimensional FSK alphabets for non coherent detection. Trellis coded, lattice coded and bit-interleaved coded modulations for non-coherent detection. An iterative non coherent APP detector is proposed. The report contains a capacity analysis for orthogonal and non orthogonal alphabets on a non coherent channel. This document is written in french.	PDF (1.6M) , PS (2.5M) , PS+GZ (663K)
Hadi Sawaya	Performance optimization for capacity-approaching channel coding schemes, March 2002.	Ph.D. report, ENST Paris, France. Directed by Joseph Boutros. A nice asymptotic comparison between spherical codes and lattice codes is given. You also find some results on turbo codes, especially symbol-based (quaternary) APP decoding. Multilevel coded modulations (MLC) are also studied as an efficient coding scheme for non binary modulations.	PDF (2.2M) , PS (2.4M) , PS+GZ (573K)
Sandrine Vialle & Joseph J. Boutros	Performance of optimal codes on Gaussian and Rayleigh fading channels: a geometrical approach, October 1999.	Paper presented at the 37^th Annual Allerton Conference, Illinois, USA. You can find in this paper how to compute the error rate limits (best codes) given the coding rate and the finite code length.	PDF (204K) , PS (470K) , PS+GZ (89K)
Joseph J. Boutros & Giuseppe Caire	Iterative multiuser joint decoding: Unified framework and asymptotic analysis, July 2002.	Paper published in the IEEE Transactions on Information Theory. This joint work with Giuseppe Caire unifies all techniques known as Turbo CDMA. Factor graphs are used to represent the coded multiple access system and iterative APP decoding is described as a sum-product algorithm. All interference cancellation (IC) algorithms are derived in a unified way. Density Evolution and Gaussian Approximation are used to determine the asymptotical CDMA system limits.	PDF (799K)
Loïc Brunel & Joseph J. Boutros	Lattice decoding for joint detection in direct-sequence CDMA systems, April 2003.	Paper published in the IEEE Transactions on Information Theory, partly published at ITW’99 in South Africa. It describes joint detection from a lattice point of view. The sphere decoder is used to jointly decode up to 63 users. It is extremely important to indicate that the sphere decoder is a maximum likelihood (ML) joint detector when CDMA is synchronous.	PDF (549K)
Joseph J. Boutros, & Nicolas Gresset	HICCUP: Bit interleaved coded modulation designed for multiple antenna channels with iterative joint detection and decoding, July 2003.	This report includes new results on precoding via rotations for multiple antenna channels, mapping optimization (both bidimensional and multi-dimensional QAM/PSK mappings) for multiple antenna channels, and soft output sphere decoding valid for all type of linear channels.	PDF (774K) , PS (953K) , PS+GZ (253K)
Joseph J. Boutros, Nicolas Gresset & Loïc Brunel	Turbo coding and decoding for multiple antenna channels, September 2003.	Paper published at the 3^rd International Symposium on Turbo Codes and Related Topics, Brest, France. The paper mainly studies bit-interleaved coded modulation for multiple antenna channels. Optimized binary QAM mappings, linear precoding via cyclotomic rotations, and a space-time binary interleaver are proposed. The genie method described in this paper simplifies some analytical computations under iterative APP detection/decoding of the space-time BICM.	PDF (204K) , PS (342K) , PS+GZ (96K)
Joseph J. Boutros, Nicolas Gresset, Loïc Brunel & Marc Fossorier	Soft-input soft-output lattice sphere decoder for linear channels, December 2003.	Paper published at Globecom’2003, San Francisco. We propose a soft-output sphere decoder based on both Pohst and Schnorr-Euchner strategies. Illustration is made via bit-interleaved coded modulation (BICM) for multiple-antenna channels (MIMO). The soft-output (list processing) sphere decoder is outside the detection/decoding loop.	PDF (164K) , PS (208K) , PS+GZ (69K)
Albert Guillén i Fàbregas	Concatenated codes for block-fading channels, June 2004.	PhD thesis, EPFL, Lausanne, Switzerland. Supervised by Giuseppe Caire. Defended in front of the following jury: Joseph J. Boutros, Giuseppe Caire, Raymond Knopp, Giorgio Taricco, Emre Telatar, and Rüdiger Urbanke.	PDF (2398K) , PS (7779K)
Nicolas Gresset	New space-time coding techniques with bit interleaved coded modulations, December 2004.	PhD thesis, ENST, Paris, France. Supervised by Loïc Brunel and Joseph J. Boutros. Defended in front of the following jury: Geneviève Baudoin, Jean-Claude Belfiore, Loïc Brunel, Raymond Knopp, Hans-Andrea Loeliger, Hikmet Sari, and Gilles Zémor.	PDF (1242K)
Various authors from North-America, Europe, and other continents.	Turbo Coding versus LDPC Coding. Updated on November 7, 2006.	I did this selection last year with my students. They used those papers in their project on Advanced Digital Communications and Coding (ADC course). I may update the list of selected papers in the coming weeks. I limited my fine selection to 11 papers on LDPC codes and 12 papers on Turbo codes. The degree of difficulty varies from simple to very difficult.	Turbo Codes versus LDPC Codes Click to visit the HTML Page
Fatma Kharrat-Kammoun	Adaptive techniques and classifications for MIMO systems, October 2006.	PhD thesis, ENST, Paris, France. Supervised by Sandrine Fontenelle, Hugues Randriambololona, and Joseph J. Boutros. Defended in front of the following jury: Ezio Biglieri, Raymond Knopp, Emre Telatar, Jean-Claude Belfiore, Hugues Randriambololona, Stéphanie Rouquette, and myself.	PDF (5.2M)
Ghassan Kraidy	Coded modulations for the multiple-antenna and cooperative fading channels, July 2007.	PhD thesis, ENST, Paris, France. Supervised by Joseph J. Boutros. Defended in front of the following jury: Inbar Fijalkow, Helmut Bölcskei, Raymond Knopp, Philippe Godlewski, Dirk Slock, Nicolas Gresset, and myself.	PDF (797K)