Date & Time: Thursday, August 13, 2015, 17:30-18:30.
Venue: Room 113
Title: A systematic local encoder for Grassmann codes and related codes
Speaker: Fernando Pinero, IIT Bombay
Abstract: We introduce the concept of an iterative encoder, which uses a short, simple code with a deletion decoder and an incidence structure to define and encode a Tanner code. Previously we discussed the structure of the parity check equations of Grassmann codes and showed how these relate to the lines of the Grassmannian in the algebraic, geometric and combinatorial way. We also proved that the Grassmann code is a Tanner code of its point line incidence graph and the simplest Grassmann code. We will prove that by taking the lines of the Grassmannian and a special subset of the Grassmannian, called an apartment, we can encode the parity check bits of the Grassmannian locally and without the need of iteration. We will further prove that this encoder also works for Schubert union codes and, if time permits, for affine Grassmann codes. Furthermore, this encoding algorithm gives also an alternative proof of the fact that the dual Grassmann code or the related code is generated by its parity check bits.