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PRODID:-//eluceo/ical//2.0/EN
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BEGIN:VEVENT
UID:www.tcs.tifr.res.in/event/1241
DTSTAMP:20230914T125956Z
SUMMARY:Binary linear error correcting codes with sufficient symmetry achie
 ve capacity on the erasure channel
DESCRIPTION:Speaker: Sreejata Kishor  Bhattacharya\n\nAbstract: \nConstruct
 ing error correcting codes that achieve Shannon capacity on a given memory
 less channel and have efficient encoding and decoding algorithms has been 
 a major line of recent research. In this talk\, we shall discuss the error
  correcting capacity of codes on the binary erasure channel. We will show 
 that sufficient symmetry alone implies a linear error correcting code achi
 eves capacity on BEC. In particular\, we shall prove the following results
 : (i) Consider a family of linear binary error correcting codes (parameter
 ized by block length) approaching constant rate. Suppose the transitive gr
 oup of each code is doubly symmetric and the distance satisfies log(distan
 ce)/log(block length)->1. Then this family achieves capacity on BEC. This 
 implies that BCH codes achieve capacity on BEC. (ii) Binary Reed Muller co
 des achieve capacity on BEC. In this proof\, we shall not use any special 
 properties of Reed Muller codes other than the fact that their symmetry gr
 oup contains GL_n(F_2) and that a family of Reed Muller codes approaching 
 constant rate satisfies log(distance)/log(block length)->1/2.\n
URL:https://www.tcs.tifr.res.in/web/events/1241
DTSTART;TZID=Asia/Kolkata:20220923T160000
DTEND;TZID=Asia/Kolkata:20220923T170000
LOCATION:A201
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