Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 12 of 12 for “"List Decoding"”.
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Local list decoding of homomorphisms
We investigate the local-list decodability of codes whose codewords are group homomorphisms. The study of such codes was intiated by Goldreich and Levin with the seminal work on decoding the Hadamard code. Many of the recent abstractions of their initial algorithm focus on Locally Decodable Codes …
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List decoding of error-correcting codes
… time, and several classical polynomial time decoding algorithms are known for specific code families. Traditionally, however, these algorithms have been constrained to output a unique codeword. Thus they faced a "combinatorial barrier" and could only correct up to d/2 errors, where d is the …
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Subspace polynomials and list decoding of Reed-Solomon codes
We show combinatorial limitations on efficient list decoding of Reed-Solomon codes beyond the Johnson and Guruswami-Sudan bounds [Joh62, Joh63, GS99]. In particular, we show that for any ... , there exist arbitrarily large fields ... * Existence: there exists a received word ... that agrees with a …
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List decoding expander-based codes via fast approximation of expanding CSPs
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01
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Analysis, improvement and extensions of a Lee metric list decoding algorithm for alternant codes
… Lee metric codes based on the Guruswami-Sudan decoding and Ido Tal algorithms are studied in this thesis. An algorithm is developped over a Galois ring, some improvements in special cases are given as for large alphabet codes and codes over GF(2). Tools are developped to study Lee metric codes …
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Learning noisy characters, multiplication codes, and cryptographic hardcore predicates
… different way. Our proof framework extends the list-decoding method of Goldreich and Levin [38] for showing hardcore predicates, by introducing a new class of error correcting codes and new list-decoding algorithm we develop for these codes. In coding theory, we introduce a novel class of error …
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Zero-error communication over adder MAC
… in random coding. 2. We determine the rate of a list-decoding version of B[subscript h]-codes achieved by the random coding method. 3. We study several related problems about Rényi entropy.
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The method of multiplicities
… of analysis has found applications in works on list-decoding of error correcting codes, constructions of randomness extractors, and in obtaining strong bounds for the size of Kakeya Sets. Remarkably, all these applications have relied on very simple and elementary properties of polynomials such …
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Gröbner basis techniques for certain problems in coding and systems theory
… approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list …
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Contributions to the decoding of linear codes over Z4
… thesis explores various hard and soft decision decoding techniques for linear codes over Z4, all of which, offer substantial coding gains over classical algebraic decoding. We focus only on codes which are free, i.e., (n, k, d) linear codes whose canonical images over GF(2) are (n, k) linear …
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Codes for Synchronization in Channels and Sources with Edits
… linear error-correcting codes and uses a list decoder. Motivated by the sequence reconstruction problem from traces in DNA-based storage, the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder is considered. A simple …