Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
125 tokens/sec
GPT-4o
47 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Erasure List-Decodable Codes from Random and Algebraic Geometry Codes (1401.2716v1)

Published 13 Jan 2014 in cs.IT and math.IT

Abstract: Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure errors. The contributions of this paper are two-fold. Firstly, we show that, for arbitrary $0<R\<1$ and $\epsilon\>0$ ($R$ and $\epsilon$ are independent), with high probability a random linear code is an erasure list decodable code with constant list size $2{O(1/\epsilon)}$ that can correct a fraction $1-R-\epsilon$ of erasures, i.e., a random linear code achieves the information-theoretic optimal trade-off between information rate and fraction of erasure errors. Secondly, we show that algebraic geometry codes are good erasure list-decodable codes. Precisely speaking, for any $0<R\<1$ and $\epsilon\>0$, a $q$-ary algebraic geometry code of rate $R$ from the Garcia-Stichtenoth tower can correct $1-R-\frac{1}{\sqrt{q}-1}+\frac{1}{q}-\epsilon$ fraction of erasure errors with list size $O(1/\epsilon)$. This improves the Johnson bound applied to algebraic geometry codes. Furthermore, list decoding of these algebraic geometry codes can be implemented in polynomial time.

Citations (5)

Summary

We haven't generated a summary for this paper yet.