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Center for Nonlinear Studies |
Ever since Shannon's seminal paper on theory of communications in 1948, coding theory has strived to achieve the fundamental limits set by Shannon. Low-density Parity-check codes (LDPC) have shown tremendous promise for fast encoding and decoding of information. However, since their inception in 1963 by Robert Gallager, it is still not known if one can construct LDPC codes which approach the Shannon limit. In this talk I will briefly outline the channel coding problem and error correcting codes based on graphs and their associated low-complexity decoding algorithm. These codes can be found in virtually any new communication standard or product. These days they can even be found in hard disk drives, a product with extremely stringent requirements. A key focus of modern coding theory is to study the interplay between the graphical structure of a code and its decoding performance. I will focus on the particular structure which emerges when codes are "coupled". We call these "spatially coupled codes". I will demonstrate that these codes hold the promise of achieving simultaneous dreams of near Shannon limit performance, good finite-length performance, practical implementability and universality (same code to be used irrespective of the nature of noisy channel).
Host: Peter Loxley, loxley@lanl.gov