AAECC/IRIT Lab

Applied Algebra and Error Correcting Codes

 
 


AAECC/IRIT : is a research team under the responsability of Professor Alain Poli, Docteur d'Etat es Mathématiques (1978).


Domains of Activity

Our domains of activity are : contracts with industry (20 from 1981 until now), publications in Applied Algebra as well as in Error Correcting Codes fields, and books.

Contracts with industry (21 up to now)

We worked with several industrial partners (local, regional, national, european) on various subjects as for example : Reed-Solomon codes (coding/decoding), Gröbner bases and decoding, codes and bursts, AI and codes, systolics and codes, convolutional codes and cheap decoders.

Publications

Among our publications the following are the most significant :
 

1980 - "Invariant codes under the group of isometries ...", by A. Poli, in Comptes Rendus de l'Académie des Sciences (CRAS), t280, série A, pp 1029-1032,
1981 - "Principal nilpotent codes, with maximal dimension, in an GF(q) algebra of a p-elementary abelian group", by A. Poli and M. Ventou, in CRAS, t296, série 1, pp 283-285.
1983 - "Construction de codes autoduaux de profondeur 1 ou 2...", by A. Poli and M. Ventou, in Annals of Discrete Mathematics, (17), pp 549-557.
1985 - "Self-dual multicirculant codes", by M. Ventou and C. Rigoni, in Discrete Mathematics, (56), n2-3, pp291-299.
1985 - "Automorphisms of principal nilpotent self-dual codes in certain modular algebras", by A. Poli and J.A. Thiong-Ly, in Discrete Mathematics (56), pp 265-273.
1988 - "A software programm for factoring polynomials over large GF(p)", by A. Poli and M.C. Gennero, in LNCS (307), pp 139-156.
1991 - "New systolic architecture for cyclic codes encoding", by M. Diab, in LNCS, (539), pp340-352.
1991 - "New bit-serial systolic multiplier for GF(2^m) using irreducible trinomials", by M. Diab and A. Poli, in Electronics Letters IEE, (27), n13, pp 1183-1185.
1991 - "Treshold decoder and two feedback checkers for nonsystematic convolutionnal code (2,1,6)", by D. Randriananja, in Electronics Letters IEE, (27), n12, pp11-112.
1994 - "A deterministic construction for normal bases in abelian extensions", by A. Poli, in Communications in Algebra, 22(12), pp4751-4757
1994 - "Shannon's entropy and pooling of experts knowledge", by A. Poli, C. Poli, in Proc. EXPERSYS'94 Conference, Houston, pp 587-592.
1995 - "Constructing SCN bases in characteristic 2", by A. Poli, in IEEE Trans. on IT, (41), n3, pp 790-793.
1995 - "A deterministic construction of normal bases with complexity O(n^3+nlognlog(logn)logq)", by A. Poli, in Journal of Symbolic Computations, (19), pp 305-319.
1996 - "An expert system for codes : SECC", by C. Poli, M.C. Gennero, A. Poli, in Proc. of ISITA'96 International Conference, Victoria (Canada), pp 826-829.
1998 - "Xin Algorithm and Grobner bases", by D. Xin, A. Poli, M.C. Gennero, in Proc. of  ISITA'98 vol 1, pp 204-208, Mexico, August 1998
1999 - "Permutation group of the q-ary image of some q^m-ary cyclic codes", by J. Lacan, E. Delpeyroux, contemporary Mathematics (225), pp165-176.
1999 - "Discrete Fourier Transform and Gröbner bases" by A. Poli, M.C. Gennero, D. Xin, LNCS vol 1719, pp 444-453.

FG-algorithm is an algebraic algorithm running  for every cyclic code over every finite field.
FG-algorithm is based on DFT as well as on Gröbner bases. Its complexity is much less than that of Chen et al.'s algorithm in 139 cases over 147.
Moreover only one attempt is needed to correct a code word, when Chen et al.'s algorithm needs several ones.
2000 - "Synchronization from roots of polynomials" by A. Poli, M.C. Gennero, ISITA nov 5-8 2000, vol 2., pp 616-619.


Books

1989 - "Codes Correcteurs d'erreurs: théorie et applications", by A. Poli and Ll. Huguet, with participation from M.C. Gennero, F. Michon,S. Potteck, J. Rifa, J.P. Rocher, B. Roy, MASSON ed. (450 pages).
1992 - "Error Correcting Codes : theory and applications", English translation from Y. Craig, Prentice Hall publications, (500 pages).
1995 - "Exercices sur les Codes Correcteurs : 600 exercices corrigés", by A. Poli, with participation from L. Bénéteau, F. Cortial, M.C. Gennero, Ll. Huguet, H. Imai, R. Kohno, J.P. Rocher, R. Rolland, MASSON ed., (220 pages).
2003- "Codage de canal" (directed by Alain Glavieux). A. Poli's contribution : block codes, finite fields, pp 67-156. Hermes Ed.
2004- "Le Sang de Le Loup", roman, Société des Ecrivains Ed. Paris.
2005 - "Algèbre et Protection de l'Information", by Alain Poli and Philippe Guillot. Hermes Ed (300 pages).
2007 - "Channel Coding in Communication Networks" (directed by Alain Glavieux, adapted from
the 2003 book). A. Poli's contribution : block codes, finite fields. Hermes Ed.

Proceedings

1985 - AAECC-1 (Discrete Math 56, 1985) Alain Poli editor
1985 - AAECC-2 (Springer Lecture Notes in Comp. sciences 228)  A. Poli ed
1987 - AAECC-5 (Springer LNCS 356) Ll. Huguet, A. Poli eds
1999 - AAECC-13 (Springer LNCS 1719) M. Fossorier, H. Imai, S. Lin, A. Poli eds
2003 - AAECC-15 (Springer LNCS 2643) M. Fossorier, T. Hoehold, A. Poli eds

        2006 - AAECC-16 (Springer LNCS 3857)  M. Fossorier, H. Imai, S. Lin, A. Poli eds
 
 
 


Further in AAECC Conferences