"ON ALGEBRAIC DECODING OF QARY REEDMULLER AND PRODUCT REEDSOLOMON CODES"
Abstract
We consider a list decoding algorithm recently proposed by PellikaanWu for qary ReedMuller codes RM{sub q}({ell}, m, n) of length n {le} q{sup m} when {ell} {le} q. A simple and easily accessible correctness proof is given which shows that this algorithm achieves a relative errorcorrection radius of {tau} {le} (1{radical}{ell}q{sup m1}/n). This is an improvement over the proof using onepoint AlgebraicGeometric decoding method given in. The described algorithm can be adapted to decode product ReedSolomon codes. We then propose a new low complexity recursive aJgebraic decoding algorithm for product ReedSolomon codes and ReedMuller codes. This algorithm achieves a relative error correction radius of {tau} {le} {Pi}{sub i=1}{sup m} (1  {radical}k{sub i}/q). This algorithm is then proved to outperform the PellikaanWu algorithm in both complexity and error correction radius over a wide range of code rates.
 Authors:
 Los Alamos National Laboratory
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 OSTI Identifier:
 984531
 Report Number(s):
 LAUR070469
TRN: US201016%%1377
 DOE Contract Number:
 AC5206NA25396
 Resource Type:
 Conference
 Resource Relation:
 Conference: ISIT 2007 ; 200706 ; NICE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 99; ALGORITHMS; ALGEBRA; LANL; COMPUTERS
Citation Formats
SANTHI, NANDAKISHORE. "ON ALGEBRAIC DECODING OF QARY REEDMULLER AND PRODUCT REEDSOLOMON CODES". United States: N. p., 2007.
Web.
SANTHI, NANDAKISHORE. "ON ALGEBRAIC DECODING OF QARY REEDMULLER AND PRODUCT REEDSOLOMON CODES". United States.
SANTHI, NANDAKISHORE. Mon .
""ON ALGEBRAIC DECODING OF QARY REEDMULLER AND PRODUCT REEDSOLOMON CODES"". United States.
doi:. https://www.osti.gov/servlets/purl/984531.
@article{osti_984531,
title = {"ON ALGEBRAIC DECODING OF QARY REEDMULLER AND PRODUCT REEDSOLOMON CODES"},
author = {SANTHI, NANDAKISHORE},
abstractNote = {We consider a list decoding algorithm recently proposed by PellikaanWu for qary ReedMuller codes RM{sub q}({ell}, m, n) of length n {le} q{sup m} when {ell} {le} q. A simple and easily accessible correctness proof is given which shows that this algorithm achieves a relative errorcorrection radius of {tau} {le} (1{radical}{ell}q{sup m1}/n). This is an improvement over the proof using onepoint AlgebraicGeometric decoding method given in. The described algorithm can be adapted to decode product ReedSolomon codes. We then propose a new low complexity recursive aJgebraic decoding algorithm for product ReedSolomon codes and ReedMuller codes. This algorithm achieves a relative error correction radius of {tau} {le} {Pi}{sub i=1}{sup m} (1  {radical}k{sub i}/q). This algorithm is then proved to outperform the PellikaanWu algorithm in both complexity and error correction radius over a wide range of code rates.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 22 00:00:00 EST 2007},
month = {Mon Jan 22 00:00:00 EST 2007}
}

We present a randomized algorithm which takes as input n distinct points ((x{sub i}, y{sub i})){sup n}{sub i=1} from F x F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., y{sub i} = f (x{sub i}) for at least t values of i), provided t = {Omega}({radical}nd). The running time is bounded by a polynomial in n. This immediately provides a maximum likelihoodmore »

General Purpose Graphics Processing Unit Based HighRate Rice Decompression and ReedSolomon Decoding
As the volume of data acquired by spacebased sensors increases, mission data compression/decompression and forward error correction code processing performance must likewise scale. This competency development effort was explored using the General Purpose Graphics Processing Unit (GPGPU) to accomplish highrate Rice Decompression and highrate ReedSolomon (RS) decoding at the satellite mission ground station. Each algorithm was implemented and benchmarked on a single GPGPU. Distributed processing across one to four GPGPUs was also investigated. The results show that the GPGPU has considerable potential for performing satellite communication Data Signal Processing, with three times or better performance improvements and up to tenmore » 
SEU hardened memory cells for a CCSDS Reed Solomon encoder
This paper reports on design technique to harden CMOS memory circuits against Single Event Upset (SEU) in the space environment. The design technique provides a recovery mechanism which is independent of the shape of the upsetting event. A RAM cell and Flip Flop design are presented to demonstrate the method. The Flip Flop was used in the control circuitry for a Reed Solomon encoder designed for the Space Station and Explorer platforms. 
FPGA Implementation of ReedSolomon Decoder for IEEE 802.16 WiMAX Systems using SimulinkSysgen Design Environment
This paper presents FPGA implementation of the ReedSolomon decoder for use in IEEE 802.16 WiMAX systems. The decoder is based on RS(255,239) code, and is additionally shortened and punctured according to the WiMAX specifications. Simulink model based on Sysgen library of Xilinx blocks was used for simulation and hardware implementation. At the end, simulation results and hardware implementation performances are presented. 
Decoding and optimized implementation of SECDED codes over GF(q)
A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a columnwise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selectingmore »