Concatenated codes can achieve list-decoding capacity

We prove that binary linear concatenated codes with an outer algebraic code (specifically, a folded Reed-Solomon code) and independently and randomly chosen linear inner codes achieve the list-decoding capacity with high probability. In particular, for any 0 < < 1/2 and > 0, there exist concatenated codes of rate at least 1 - H() - that are (combinatorially) list-decodable up to a fraction of errors. (The best possible rate, aka list-decoding capacity, for such codes is 1 - H(), and is achieved by random codes.) A similar result, with better list size guarantees, holds when the outer code is also randomly chosen. Our methods and results extend to the case when the alphabet size is any fixed prime power q 2. Our result shows that despite the structural restriction imposed by code concatenation, the family of concatenated codes is rich enough to include capacity achieving listdecodable codes. This provides some encouraging news for tackling the problem of constructing expli...

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Venkatesan Guruswami, Atri Rudra
• Keywords: Algorithms, Concatenated Codes, Linear Concatenated Codes, Linear Inner Codes, SODA 2008