Poäng: 5.0 Betygskala: TH. Valfri för: D4, E4. Kursansvarig: Universitetslektor Mats Cedervall.. Rekommenderade förkunskaper: Informationsteori (EDI030), Digitalteknik (EIT020).. Prestationsbedömning: Godkänt projekt är ett krav för att få tentera. Den skriftliga tentamen (5 tim) är av problemlösningstyp. Som ett alternativ erbjuds möjligheten till muntlig tentamen. Webbsida: http://www.it.lth.se/ecc Övrigt: Kursen kan komma att ges på engelska.

Mål:
Error control coding should protect digital data against errors which occur during transmission over a noisy communication channel or during storage in an unreliable memory. The last decade has been characterized by not only an exceptional increase in data transmission and storage but also in a rapid development in microelectronics providing us with both a need for and the possibility to implement sophisticated algorithms for error control.

Innehåll:
Introduction: Why error control? Block codes - a primer, a first encounter with convolutional codes, block codes vs. convolutional codes.
Convolutional encoders - structural properties: Convolutional codes and their encoders, the Smith form of polynomial encoding matrices, equivalent and basic encoding matrices, minimal - basic and minimal encoding matrices, minimal encoders, syndrome formers and dual encoders, systematic encoders.
Distance properties of convolutional codes: Distance measures, distances for cascaded convolutional codes, upper and lower bounds on the free distance, lower bound on the distance profile, path enumeration.
Viterbi decoding: The Viterbi algorithm, error probability bounds for convolutional codes, quantization of channel outputs.
List decoding: Decoding with limited resources, list decoding (algorithm, error probability bounds).
Sequential decoding: The Fano metric, the Stack algorithm, computational analysis, the Fano algorithm.
Convolutional encoders with good distance properties: Computing distance spectrum (FAST), some classes of rate R = 1/2 encoders.
Block codes: Reed-Solomon (RS) codes, cyclic codes, discrete Fourier transforms, decoding RS codes (the Berlekamp-Massey algorithm), erasures and errors decoding.
Trellis coded modulation: Band-limited channels and QAM, coding fundamentals, lattice-type trellis codes, geometrically uniform trellis codes, decoding of modulation codes, precoding.

Litteratur:
Johannesson, R, Zigangirov, KSh: Fundamentals of Convolutional Coding, IEEE Press, 1999.