Coding for the Operator Channel
Author
Term
4. term
Education
Publication year
2012
Submitted on
2012-06-01
Pages
102
Abstract
The topic of coding over the operator channel by means of subspace codes is considered in this thesis. This channel model and codes are motivated by random linear network coding. We first study a class of codes known as Koetter-Kschischang (KK) codes, whose definition parallels the definition of Reed- Solomon codes in classical coding theory. Various properties of KK-codes are shown, including the result that they approach the Singleton bound asymptotically. Decoding algorithms for KK-codes are also investigated. Furthermore, list decoding of subspace codes is considered. The codes introduced by Mahdavifar and Vardy, called MV-codes, are presented, and their list decoding capabilities are shown, along with correctness of the decoding. Finally, we study the problem of decoding using the theory of modules from abstract algebra.
The topic of coding over the operator channel by means of subspace codes is considered in this thesis. This channel model and codes are motivated by random linear network coding. We first study a class of codes known as Koetter-Kschischang (KK) codes, whose definition parallels the definition of Reed- Solomon codes in classical coding theory. Various properties of KK-codes are shown, including the result that they approach the Singleton bound asymptotically. Decoding algorithms for KK-codes are also investigated. Furthermore, list decoding of subspace codes is considered. The codes introduced by Mahdavifar and Vardy, called MV-codes, are presented, and their list decoding capabilities are shown, along with correctness of the decoding. Finally, we study the problem of decoding using the theory of modules from abstract algebra.
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