Algorithmic Results in List Decoding introduces and motivates the problem of list decoding, and discusses the central algorithmic results of the subject, culminating with the recent results on achieving "list decoding capacity." The main technical focus is on giving a complete presentation of the recent algebraic results achieving list decoding capacity, while pointers or brief descriptions are provided for other works on list decoding. Algorithmic Results in List Decoding is intended for scholars and graduate students in the fields of theoretical computer science and information theory. The...

How can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the rich theory of error-correcting codes . This theory has traditionally gone hand in hand with the algorithmic theory of decoding that tackles the problem of recovering from the errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally, itshowshowthenotionof list-decoding can be...