List decoding performance of algebraic geometric codes

Abstract

An efficient list decoder for algebraic geometric (AG) codes has been developed based on the mathematical framework of the Guruswami-Sudan algorithm. New simulation results presented show that coding gains of up to 1.5 dB over unique AG decoding algorithms are possible on the AWGN and Rayleigh fading channels.

List Decoding

“…These can be imposed by the iterative polynomial construction algorithm [9,11,17] in C M iterations. Notice that (5.109)) and (5.110)) have the same expression as (5.45) and (5.46), respectively, with the exception that n = q 3/2 .…”

“…Interpolation builds the minimal polynomial Q ∈ F q [x, y, z], which has a zero of multiplicity of at least m over the n interpolated units. Q can be written as: Q = a,b Q ab φ a z b , where Q ab ∈ GF(q) and φ a is a set of rational functions with pole orders up to a[17][18][19]. If (p i , r i )…”

Efficient Factorisation Algorithm for List Decoding Algebraic-Geometric and Reed-Solomon Codes

“…Wu and Siegel [12] extended [11] to an algebraic function field to list decode AG codes. In order to design an efficient list decoder for RS and AG codes, the authors have studied both the algorithms in [11] and [12], and presented the first list decoding simulation results of AG codes in [13]. It is obvious to use [11] to be extended to AG codes and [12] is based on this extension.…”