Titlebook: List Decoding of Error-Correcting Codes; Winning Thesis of th Venkatesan Guruswami Book 2005 Springer-Verlag Berlin Heidelberg 2005 Code.Er

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1 Introduction channel is “noisy” and distorts the message during transmission. The problem of reliable communication of information over such a noisy channel is a fundamental and challenging one. Error-correcting codes (or simply, codes) are objects designed to cope with this problem. They are now ubiquitous and

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2 Preliminaries and Monograph Structure the fundamental code families and constructions that will be dealt with and used in this book. Finally, we discuss the structure of this work and the main results which are established in the technical chapters that follow, explaining in greater detail how the results of the various chapters fit to

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4 Limits to List Decodabilitying radius (in other words, every Hamming ball of radius up to the Johnson radius has “few” codewords). This result plays an important role in the development of the subject of list decoding. Indeed, by showing that any code with large distance has large list decoding radius, it raises algorithmic q

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7 A Unified Framework for List Decoding of Algebraic Codesng to the importance of these codes, these results can be viewed as providing strong evidence to the general utility of list decoding as an algorithmic notion. Indeed, as we shall see in future chapters, they set the stage for a whole body of results about list decoding.

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A GMD Decoding of Concatenated Codesparticular implies an efficient algorithm to decode concatenated codes up to the product bound provided there exists an efficient errors-and-erasures decoding algorithm for the outer code, and the decoding of the inner codes can also be performed efficiently (which is usually easy since the dimensio

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