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SPCoding School The São Paulo Coding School Forum 2014-12-19T22:31:17+00:00 https://ime.unicamp.br/spcodingschool/forum/feed.php?f=7 2014-12-19T22:31:17+00:00 2014-12-19T22:31:17+00:00 https://ime.unicamp.br/spcodingschool/forum/viewtopic.php?t=27&p=43#p43 <![CDATA[Open Problems • The Simplex Conjecture]]>
The (weak) simplex conjecture in communication theory states that the best signal set with n+1 vectors in R^n for transmission over an AWGN channel under the constraint that all vectors have the same norm is the regular simplex centered at the origin.

The strong simplex conjecture stated that this was also true under an average energy constraint. However, the strong simplex has been disproved. It has been shown by Steiner that there is a signal with n+1 = 7 vectors that performs better than the regular simplex. Nevertheless, the weak version of the conjecture remains open.

Please see the .pdf files attached for more information.

Statistics: Posted by Antonio Campello — Fri Dec 19, 2014 10:31 pm

]]> 2014-12-17T00:15:05+00:00 2014-12-17T00:15:05+00:00 https://ime.unicamp.br/spcodingschool/forum/viewtopic.php?t=6&p=42#p42 <![CDATA[Open Problems • Re: Library of decoders]]> Statistics: Posted by jjauhien — Wed Dec 17, 2014 12:15 am

]]> 2014-11-24T17:47:11+00:00 2014-11-24T17:47:11+00:00 https://ime.unicamp.br/spcodingschool/forum/viewtopic.php?t=6&p=6#p6 <![CDATA[Open Problems • Library of decoders]]> Decoders_Library.pdfDespite the fact that Maximal Likelihood (ML) decoders and Nearest Neighbor (NN) decoders are easy to describe, they are in general extremely difficult to be implemented. It the most common
setting, considering a k-dimensional linear code in an n-dimensional vector space (over a finite field) a search algorithm for syndrome decoding involves a list of the size that increases exponnetially with n-k.

Small values of n are suitable for situations with strong constrains at block length and for research proposes, since actually listing decoders is essential for computing many of the important invariants (such as error probability).

The main goal of this project is to create a library of ML and NN decoders for use with software for numerical analysis, such as Mathematica, Maple, Matlab, etc.

Statistics: Posted by mfirer — Mon Nov 24, 2014 5:47 pm

]]> 2014-11-24T15:02:23+00:00 2014-11-24T15:02:23+00:00 https://ime.unicamp.br/spcodingschool/forum/viewtopic.php?t=4&p=4#p4 <![CDATA[Open Problems • Matching Channels and Metrics]]> Matching Channels and Metrics.pdfThe most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel.

Back over 40 years, in a paper from 1971. Chiang and Wolf attribute the general question of matching metrics and channels to notes from a 1967 course given by Massey. The most significant work on this question was done by Seguin in 1980, in a paper where he studies necessary and sufficient conditions for a discrete memoryless channel to be matched to an additive metric.

Considering non-additive metrics, this question is widely open, some possible approaches for binnary asymmetric channels are proposed here.

Statistics: Posted by mfirer — Mon Nov 24, 2014 3:02 pm

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