DOCSLIB.ORG

Implementation and Evaluation of Polar Codes in 5G

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Implementation and Evaluation of Polar Codes in 5G Implementation and evaluation of Polar Codes in 5G Implementation och evaluering av Polar Codes för 5G Tobias Rosenqvist Joël Sloof Faculty of Health, Science and Technology Computer Science 15 hp Supervisor: Stefan Alfredsson Examiner: Kerstin Andersson Date: 2019-06-12 Serial number: N/A Implementation and evaluation of Polar Codes in 5G Tobias Rosenqvist, Joël Sloof © 2019 The author(s) and Karlstad University This report is submitted in partial fulfillment of the requirements for the Bachelor’s degree in Computer Science. All material in this report which is not our own work has been identified and no material is included for which a degree has previously been conferred. Tobias Rosenqvist Joël Sloof Approved, Date of defense Advisor: Stefan Alfredsson Examiner: Kerstin Andersson iii Abstract In today’s society the ability to communicate with one another has grown, were a lot of focus is aimed towards speed in the telecommunication industry. For transmissions to become even faster, there are many ways to enhance transmission speeds of which error correction is one. Padding messages such that they are protected from noise, while using as few bits as possible and ensuring safe transmit is handled by error correction codes. Short codes with low complexity is a solution to faster transmission speeds. An error correction code which has gained a lot of attention since its first appearance in 2009 is Polar Codes. Polar Codes was chosen as the 3GPP standard for 5G control channel. The goal of the thesis is to develop and implement Polar Codes and rate matching according to the 3GPP standard 38.212. Polar Codes are then to be evaluated with different block sizes and rate matching settings. Finally Polar Code is compared with Convolutional code in a LTE-simulation environment. The performance evaluations are presented using BLER/(Eb=N0)-graphs. In this thesis a Polar encoder, rate matching and a Polar decoder (with Successive Can- cellation algorithm) were successfully implemented. The simulation results show that Polar Codes performs better with longer block sizes and also has a better BLER-performance than Convolutional Codes when given the same message lengths. v Contents 1 Introduction 1 1.1 Thesis goal ................................... 2 1.2 Results ...................................... 3 1.2.1 Expected results ............................ 3 1.2.2 Actual results .............................. 3 1.3 Thesis outline .................................. 3 2 Background 4 2.1 Introduction ................................... 4 2.2 Mobile broadband ............................... 5 2.2.1 Long Term Evolution .......................... 5 2.2.2 New Radio ............................... 5 2.3 Noise channels ................................. 6 2.3.1 AWGN ................................. 7 2.4 Phase-shift keying ............................... 8 2.5 Channel capacity ................................ 9 2.6 Interleaving ................................... 9 2.7 Rate matching ................................. 9 2.8 Error correction code .............................. 10 2.8.1 Convolutional Codes .......................... 10 2.8.2 Polar Codes ............................... 11 2.9 Eb=N0 ...................................... 11 2.10 Block error rate ................................. 11 2.11 MATLAB .................................... 12 2.12 Summary .................................... 12 vi 3 Project Design 13 3.1 Introduction ................................... 13 3.2 Convolutional Codes .............................. 14 3.3 Polar encoder .................................. 15 3.3.1 3GPP 38.212 .............................. 15 3.3.2 Encoding and channel polarisation .................. 16 3.4 Rate matching ................................. 19 3.4.1 Sub-block interleaving ......................... 19 3.4.2 Bit selection ............................... 20 3.5 Rate dematching ................................ 21 3.5.1 Bit deselection ............................. 21 3.5.2 Sub-block deinterleaving ........................ 22 3.6 Polar decode .................................. 22 3.6.1 Belief .................................. 23 3.6.2 Frozen bits ............................... 23 3.7 Successive Cancellation ............................. 24 3.7.1 Leaf state ................................ 25 3.7.2 Left state ................................ 26 3.7.3 Right state ............................... 26 3.7.4 Up state ................................. 27 3.8 Simulation .................................... 27 3.8.1 Parameters ............................... 28 3.8.2 Performance comparisons ....................... 29 3.9 Summary .................................... 29 4 Project Implementation 30 4.1 Introduction ................................... 30 4.2 Convolutional Codes .............................. 30 vii 4.3 Polar encoder .................................. 30 4.3.1 encode_polar.m ............................ 31 4.3.2 getReliabilitySeq.m ........................... 33 4.3.3 PolarEncode.m ............................. 33 4.3.4 getGn.m ................................. 34 4.4 Rate matching ................................. 35 4.4.1 rateMatch_polar.m ........................... 35 4.4.2 subBlock_interleaver.m ........................ 36 4.4.3 bit_selection.m ............................. 37 4.4.4 bit_interleaving.m ........................... 37 4.5 Rate dematching ................................ 38 4.5.1 DerateMatch_polar.m ......................... 39 4.5.2 bit_Deinterleaving.m .......................... 40 4.5.3 bit_Deselection.m ........................... 40 4.5.4 subBlock_Deinterleaver.m ....................... 41 4.6 Polar decoder: Successive Cancellation .................... 42 4.6.1 decode_polar.m ............................ 43 4.6.2 SC_Decode.m ............................. 45 4.6.3 SC_Decode_Node.m .......................... 46 4.7 Simulation .................................... 48 4.8 Summary .................................... 50 5 Results 51 5.1 Introduction ................................... 51 5.2 Polar Codes: Successive Cancellation performance .............. 51 5.3 Rate matching with repetition ......................... 52 5.4 Rate matching with puncturing ........................ 54 5.5 Rate matching with shortening ........................ 55 viii 5.6 Polar Codes vs Convolutional Codes ..................... 56 5.7 Summary .................................... 58 6 Conclusion 59 6.1 Introduction ................................... 59 6.2 Thesis evaluation ................................ 59 6.3 Future work ................................... 60 ix List of Figures 2.1 Effect of AWGN on a Signal of5 dB ..................... 7 2.2 Constellation diagram of 8-PSK (left) and BPSK (right) .......... 8 3.1 Simulation chain ................................ 13 3.2 Convolutional Codes design .......................... 14 3.3 Simulation chain, encoding block highlighted ................. 15 3.4 B-DMC channel ................................. 17 3.5 Polarisation of W into N virtual channels, Un: input bit, Gn: see equa- tion 3.5, Xn: bit after encoding, Yn: received bit ............... 17 3.6 Polarisation of W using G2 .......................... 18 3.7 Simulation chain, rate matching highlighted ................. 19 3.8 Bit selection: repetition, puncturing, shortening ............... 20 3.9 Simulation chain, rate dematching highlighted ................ 21 3.10 Simulation chain, decoding block highlighted ................. 22 3.11 Successive Cancellation binary tree, L(n) is beliefs in node where n is number of beliefs. u^i represent a decoded bit and 0:s are frozen bits. ........ 24 3.12 Pre-order depth-first binary tree ........................ 24 3.13 Simulation chain, included blocks highlighted ................ 27 4.1 Simulation chain, encode block highlighted .................. 30 4.2 Polar Encoding file scheme ........................... 31 4.3 MATLAB code for encode_polar CRC calculation .............. 32 4.4 MATLAB code for encode_polar, mapping information bits to reliable vir- tual channels .................................. 32 4.5 MATLAB code for getReliabilitySeq, collect the reliability sequence of size N ........................................ 33 4.6 MATLAB code for PolarEncode, encoding u_bits .............. 34 4.7 MATLAB code for getGn, generating Gi ................... 34 x 4.8 Simulation chain, rate matching block highlighted .............. 35 4.9 Rate matching file scheme ........................... 35 4.10 MATLAB code for subBlock_interleaver ................... 36 4.11 MATLAB code for bit_selection ........................ 37 4.12 MATLAB code for bit_interleaving ...................... 38 4.13 Simulation chain, rate dematching block highlighted ............. 38 4.14 Rate dematching file scheme .......................... 39 4.15 MATLAB code for bit_Deselection ...................... 41 4.16 MATLAB code for subBlock_Deinterleaver .................. 42 4.17 Simulation chain, Polar decoding block highlighted ............. 42 4.18 Decoding file scheme for Successive Cancellation ............... 43 4.19 MATLAB code for decode_polar ....................... 44 4.20 MATLAB code for SC_Decode ........................ 45 4.21 MATLAB code from SC_Decode_Node, leaf operation ........... 47 4.22 MATLAB code from SC_Decode_Node, left/right/up part. Functions SplitLeft and SplitRight are code derived from equation 3.7 and 3.9 ........ 48 4.23 MATLAB code from variable initialisation in testEnvironment ....... 49 4.24 MATLAB code
Load more

Recommended publications
  • Recommendation Itu-R Bt.2016*
    Recommendation ITU-R BT.2016 (04/2012) Error-correction, data framing, modulation and emission methods for terrestrial multimedia broadcasting for mobile reception using handheld receivers in VHF/UHF bands BT Series Broadcasting service (television) ii Rec. ITU-R BT.2016 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio-frequency spectrum by all radiocommunication services, including satellite services, and carry out studies without limit of frequency range on the basis of which Recommendations are adopted. The regulatory and policy functions of the Radiocommunication Sector are performed by World and Regional Radiocommunication Conferences and Radiocommunication Assemblies supported by Study Groups. Policy on Intellectual Property Right (IPR) ITU-R policy on IPR is described in the Common Patent Policy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1. Forms to be used for the submission of patent statements and licensing declarations by patent holders are available from http://www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found. Series of ITU-R Recommendations (Also available online at http://www.itu.int/publ/R-REC/en) Series Title BO Satellite delivery BR Recording for production, archival and play-out; film for television BS Broadcasting service (sound) BT Broadcasting service (television) F Fixed service M Mobile, radiodetermination, amateur and related satellite services P Radiowave propagation RA Radio astronomy RS Remote sensing systems S Fixed-satellite service SA Space applications and meteorology SF Frequency sharing and coordination between fixed-satellite and fixed service systems SM Spectrum management SNG Satellite news gathering TF Time signals and frequency standards emissions V Vocabulary and related subjects Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1.
    [Show full text]
  • ACRONYMS and ABBREVIATIONS BLUETOOTH SPECIFICATION Version 1.1 Page 914 of 1084
    Appendix III ACRONYMS AND ABBREVIATIONS BLUETOOTH SPECIFICATION Version 1.1 page 914 of 1084 Appendix III - Acronyms 914 22 February 2001 BLUETOOTH SPECIFICATION Version 1.1 page 915 of 1084 Appendix III - Acronyms List of Acronyms and Abbreviations Acronym or Writing out in full Which means abbreviation ACK Acknowledge ACL link Asynchronous Connection-Less Provides a packet-switched con- link nection.(Master to any slave) ACO Authenticated Ciphering Offset AM_ADDR Active Member Address AR_ADDR Access Request Address ARQ Automatic Repeat reQuest B BB BaseBand BCH Bose, Chaudhuri & Hocquenghem Type of code The persons who discovered these codes in 1959 (H) and 1960 (B&C) BD_ADDR Bluetooth Device Address BER Bit Error Rate BT Bandwidth Time BT Bluetooth C CAC Channel Access Code CC Call Control CL Connectionless CODEC COder DECoder COF Ciphering Offset CRC Cyclic Redundancy Check CVSD Continuous Variable Slope Delta Modulation D DAC Device Access Code DCE Data Communication Equipment 22 February 2001 915 BLUETOOTH SPECIFICATION Version 1.1 page 916 of 1084 Appendix III - Acronyms Acronym or Writing out in full Which means abbreviation DCE Data Circuit-Terminating Equip- In serial communications, DCE ment refers to a device between the communication endpoints whose sole task is to facilitate the commu- nications process; typically a modem DCI Default Check Initialization DH Data-High Rate Data packet type for high rate data DIAC Dedicated Inquiry Access Code DM Data - Medium Rate Data packet type for medium rate data DTE Data Terminal Equipment In serial communications, DTE refers to a device at the endpoint of the communications path; typi- cally a computer or terminal.
    [Show full text]
  • Applicability of the Julia Programming Language to Forward Error-Correction Coding in Digital Communications Systems
    Applicability of the Julia Programming Language to Forward Error-Correction Coding in Digital Communications Systems A project presented to Department of Computer and Information Sciences State University of New York Polytechnic Institute At Utica/Rome Utica, New York In partial fulfillment Of the requirements of the Master of Science Degree by Ryan Quinn May 2018 Declaration I declare that this project is my own work and has not been submitted in any form for another degree of diploma at any university of other institute of tertiary education. Information derived from published and unpublished work of others has been acknowledged in the text and a list of references given. _ Ryan Quinn 2 | P a g e SUNY POLYTECHNIC INSTITUTE DEPARTMENT OF COMPUTER AND INFORMATION SCIENCES Approved and recommended for acceptance as a project in partial fulfillment of the requirements for the degree of Master of Science in computer and information science _ DATE _ Dr. Bruno R. Andriamanalimanana Advisor _ Dr. Saumendra Sengupta _ Dr. Scott Spetka 3 | P a g e 1 ABSTRACT Traditionally SDR has been implemented in C and C++ for execution speed and processor efficiency. Interpreted and high-level languages were considered too slow to handle the challenges of digital signal processing (DSP). The Julia programming language is a new language developed for scientific and mathematical purposes that is supposed to write like Python or MATLAB and execute like C or FORTRAN. Given the touted strengths of the Julia language, it bore investigating as to whether it was suitable for DSP. This project specifically addresses the applicability of Julia to forward error correction (FEC), a highly mathematical topic to which Julia should be well suited.
    [Show full text]
  • 16.548 Notes 15: Concatenated Codes, Turbo Codes and Iterative Processing Outline
    16.548 Notes 15: Concatenated Codes, Turbo Codes and Iterative Processing Outline ! Introduction " Pushing the Bounds on Channel Capacity " Theory of Iterative Decoding " Recursive Convolutional Coding " Theory of Concatenated codes ! Turbo codes " Encoding " Decoding " Performance analysis " Applications ! Other applications of iterative processing " Joint equalization/FEC " Joint multiuser detection/FEC Shannon Capacity Theorem Capacity as a function of Code rate Motivation: Performance of Turbo Codes. Theoretical Limit! ! Comparison: " Rate 1/2 Codes. " K=5 turbo code. " K=14 convolutional code. ! Plot is from: L. Perez, “Turbo Codes”, chapter 8 of Trellis Coding by C. Schlegel. IEEE Press, 1997. Gain of almost 2 dB! Power Efficiency of Existing Standards Error Correction Coding ! Channel coding adds structured redundancy to a transmission. mxChannel Encoder " The input message m is composed of K symbols. " The output code word x is composed of N symbols. " Since N > K there is redundancy in the output. " The code rate is r = K/N. ! Coding can be used to: " Detect errors: ARQ " Correct errors: FEC Traditional Coding Techniques The Turbo-Principle/Iterative Decoding ! Turbo codes get their name because the decoder uses feedback, like a turbo engine. Theory of Iterative Coding Theory of Iterative Coding(2) Theory of Iterative Coding(3) Theory of Iterative Coding (4) Log Likelihood Algebra New Operator Modulo 2 Addition Example: Product Code Iterative Product Decoding RSC vs NSC Recursive/Systematic Convolutional Coding Concatenated Coding
    [Show full text]
  • Improving Wireless Link Throughput Via Interleaved FEC
    Improving Wireless Link Throughput via Interleaved FEC Ling-Jyh Chen, Tony Sun, M. Y. Sanadidi, Mario Gerla UCLA Computer Science Department, Los Angeles, CA 90095, USA {cclljj, tonysun, medy, gerla}@cs.ucla.edu Abstract Traditionally, one of three techniques is used for er- ror-control: 1) Retransmission which uses acknowl- Wireless communication is inherently vulnerable to edgements, and time-outs; 2) Redundancy, and 3) Inter- errors from the dynamic wireless environment. Link leaving [6] [13]. Retransmitting lost packets is an obvi- layer packets discarded due to these errors impose a ous means by which error may be repaired, and it is serious limitation on the maximum achievable through- typically performed at either the link layer with Auto- put in the wireless channel. To enhance the overall matic Repeat reQuest (ARQ) or at the end-to-end layers throughput of wireless communication, it is necessary to with protocols like TCP. When data is exchanged have a link layer transmission scheme that is robust to through a relatively error-free communication medium, the errors intrinsic to the wireless channel. To this end, retransmission is clearly a good tactic. However, re- we present Interleaved-Forward Error Correction (I- transmission is not the best strategy in an error-prone FEC), a clever link layer coding scheme that protects communication channel, where high latency and band- link layer data against random and busty errors. We width overhead are believed to make retransmission a examine the level of data protection provided by I-FEC less than ideal error controlling technique. against other popular schemes. We also simulate I-FEC Redundancy is the means by which repair data is in Bluetooth, and compare the TCP throughput result added along with the original data, such that corrupted with Bluetooth’s integrated FEC coding feature.
    [Show full text]
  • LDPC Decoder Design Using Compensation Scheme of Group Comparison for 5G Communication Systems
    electronics Article LDPC Decoder Design Using Compensation Scheme of Group Comparison for 5G Communication Systems Chen-Hung Lin 1,2,* , Chen-Xuan Wang 2 and Cheng-Kai Lu 3 1 Biomedical Engineering Research Center, Yuan Ze University, Jungli 32003, Taiwan 2 Department of Electrical Engineering, Yuan Ze University, Jungli 32003, Taiwan; [email protected] 3 Department of Electrical and Electronic Engineering, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia; [email protected] * Correspondence: [email protected] Abstract: This paper presents a dual-mode low-density parity-check (LDPC) decoding architec- ture that has excellent error-correcting capability and a high parallelism design for fifth-generation (5G) new-radio (NR) applications. We adopted a high parallelism design using a layered decoding schedule to meet the high throughput requirement of 5G NR systems. Although the increase in parallelism can efficiently enhance the throughput, the hardware implementation required to support high parallelism is a significant hardware burden. To efficiently reduce the hardware burden, we used a grouping search rather than a sorter, which was used in the minimum finder with decoding performance loss. Additionally, we proposed a compensation scheme to improve the decoding per- formance loss by revising the probabilistic second minimum of a grouping search. The post-layout implementation of the proposed dual-mode LDPC decoder is based on the Taiwan Semiconduc- Citation: Lin, C.-H.; Wang, C.-X.; Lu, tor Manufacturing Company (TSMC) 40 nm complementary metal-oxide-semiconductor (CMOS) C.-K. LDPC Decoder Design Using Compensation Scheme of Group technology, using a compensation scheme of grouping comparison for 5G communication systems Comparison for 5G Communication with a working frequency of 294.1 MHz.
    [Show full text]
  • Burst Correction Coding from Low-Density Parity-Check Codes
    BURST CORRECTION CODING FROM LOW-DENSITY PARITY-CHECK CODES by Wai Han Fong A Dissertation Submitted to the Graduate Faculty of George Mason University In Partial fulfillment of The Requirements for the Degree of Doctor of Philosophy Electrical and Computer Engineering Committee: Dr. Shih-Chun Chang, Dissertation Director Dr. Shu Lin, Dissertation Co-Director Dr. Geir Agnarsson, Committee Member Dr. Bernd-Peter Paris, Committee Member Dr. Brian Mark, Committee Member Dr. Monson Hayes, Department Chair Dr. Kenneth S. Ball, Dean, The Volgenau School of Engineering Date: Fall Semester 2015 George Mason University Fairfax, VA Burst Correction Coding from Low-Density Parity-Check Codes A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at George Mason University By Wai Han Fong Master of Science George Washington University, 1992 Bachelor of Science George Washington University, 1984 Director: Dr. Shih-Chun Chang, Associate Professor Department of Electrical and Computer Engineering George Mason University Fairfax, VA Co-Director: Dr. Shu Lin, Professor Department of Electrical and Computer Engineering University of California Davis, CA Fall Semester 2015 George Mason University Fairfax, Virginia Copyright c 2015 by Wai Han Fong All Rights Reserved ii Dedication I dedicate this dissertation to my beloved parents, Pung Han and Soo Chun; my wife, Ellen; children, Corey and Devon; and my sisters, Rose and Agnes. iii Acknowledgments I would like to express my sincere gratitude to my two Co-Directors: Shih-Chun Chang and Shu Lin without whom this would not be possible. In addition, I would especially like to thank Shu Lin for his encouragement, his creativity and his generosity, all of which are an inspiration to me.
    [Show full text]
  • Performance Analysis and Design of MIMO-OFDM System Using Concatenated Forward Error Correction Codes
    J. Cent. South Univ. (2017) 24: 1322−1343 DOI: 10.1007/s11771-017-3537-2 Performance analysis and design of MIMO-OFDM system using concatenated forward error correction codes Arun Agarwal1, Saurabh N. Mehta2 1. PhD Scholar, School of Electrical Engineering, Department of Information Technology, AMET University, Tamil Nadu, Chennai 603112, India; 2. Department of Electronics and Telecommunication Engineering, Vidyalankar Institute of Technology, Mumbai-400037, Maharashtra, India © Central South University Press and Springer-Verlag Berlin Heidelberg 2017 Abstract: This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), quadrature amplitude modulation (QAM)-16 and QAM-64 with four error correction codes (convolutional code (CC), Reed-Solomon code (RSC)+CC, low density parity check (LDPC)+CC, Turbo+CC) is studied under three channel models (additive white Guassian noise (AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate (BER) and the peak signal to noise ratio (PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance. Key words: bit error rate (BER); convolutional code (CC); forward error correction; peak signal to noise ratio (PSNR); Turbo code signal reliability as well as the multiple transmissions, 1 Introduction without extra radiation and spectrum bandwidth [6−9].
    [Show full text]
  • CRC-Assisted Error Correction in a Convolutionally Coded System Renqiu Wang, Member, IEEE, Wanlun Zhao, Member, IEEE, and Georgios B
    IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 11, NOVEMBER 2008 1807 CRC-Assisted Error Correction in a Convolutionally Coded System Renqiu Wang, Member, IEEE, Wanlun Zhao, Member, IEEE, and Georgios B. Giannakis, Fellow, IEEE Abstract—In communication systems employing a serially When the signal to noise ratio (SNR) is relatively high, only a concatenated cyclic redundancy check (CRC) code along with small number of errors are typically present in an erroneously a convolutional code (CC), erroneous packets after CC decoding decoded packet. Instead of discarding the entire packet, the are usually discarded. The list Viterbi algorithm (LVA) and the iterative Viterbi algorithm (IVA) are two existing approaches theme is this paper is to possibly recover it by utilizing jointly capable of recovering erroneously decoded packets. We here ECC and CRC. employ a soft decoding algorithm for CC decoding, and introduce We will study a system with serially concatenated CRC and several schemes to identify error patterns using the posterior CC (CRC-CC). Being a special case of conventional serially information from the CC soft decoding module. The resultant iterative decoding-detecting (IDD) algorithm improves error concatenated codes (CSCC) [1], CRC-CC has been widely performance by iteratively updating the extrinsic information applied in wireless communications, for example, in an IS-95 based on the CRC parity check matrix. Assuming errors only system. Various approaches are available to recover erroneous happen in unreliable bits characterized by small absolute values packets following the Viterbi decoding stage. One of them is of the log-likelihood ratio (LLR), we also develop a partial IDD based on the list Viterbi algorithm (LVA), which produces a (P-IDD) alternative which exhibits comparable performance to IDD by updating only a subset of unreliable bits.
    [Show full text]
  • Low Density Parity Check Encoder and Decoder on Silago Coarse Grain Reconfigurable Architecture
    DEGREE PROJECT IN ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 Low Density Parity Check Encoder and Decoder on SiLago Coarse Grain Reconfigurable Architecture WEIJIANG KONG KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Abstract Low density parity check (LDPC) code is an error correction code that has been widely adopted as an optional error correcting operation in most of today’s communication protocols. Current design of ASIC or FPGA based LDPC accelerators can reach Gbit/s data rate. However, the hardware cost of ASIC based methods and related interface is considerably high to be integrated into coarse grain reconfigurable architectures (CGRA). Moreover, for platforms aiming at high level synthesis or system level synthesis, they don’t provide flexibility under low-performance low-cost design scenarios. In this degree project, we establish connectivity between SiLago CGRA and a typical QC-LDPC code defined in IEEE 802.11n standard. We design lightweight LDPC encoder and decoder blocks using FSM+Datapath design pattern. The encoder provides sufficient throughput and consumes very little area and power. The decoder provides sufficient performance for low speed modulations while consuming significantly lower hardware resources. Both encoder and decoder are capable of cooperating with SiLago based DRRA through standard Network on Chip (NOC) based shared memory, DiMArch. And extra hardware for interface is no longer necessary. We verified our design through RTL simulation and synthesis. Encoder went through logic and physical synthesis while decoder went through only logic synthesis. The result acquired proves that our design is closely coupled with the SiLago CGRA while provides a solution with low- performance and low-cost.
    [Show full text]
  • Reed-Solomon Encoding and Decoding
    Bachelor's Thesis Degree Programme in Information Technology 2011 León van de Pavert REED-SOLOMON ENCODING AND DECODING A Visual Representation i Bachelor's Thesis | Abstract Turku University of Applied Sciences Degree Programme in Information Technology Spring 2011 | 37 pages Instructor: Hazem Al-Bermanei León van de Pavert REED-SOLOMON ENCODING AND DECODING The capacity of a binary channel is increased by adding extra bits to this data. This improves the quality of digital data. The process of adding redundant bits is known as channel encod- ing. In many situations, errors are not distributed at random but occur in bursts. For example, scratches, dust or fingerprints on a compact disc (CD) introduce errors on neighbouring data bits. Cross-interleaved Reed-Solomon codes (CIRC) are particularly well-suited for detection and correction of burst errors and erasures. Interleaving redistributes the data over many blocks of code. The double encoding has the first code declaring erasures. The second code corrects them. The purpose of this thesis is to present Reed-Solomon error correction codes in relation to burst errors. In particular, this thesis visualises the mechanism of cross-interleaving and its ability to allow for detection and correction of burst errors. KEYWORDS: Coding theory, Reed-Solomon code, burst errors, cross-interleaving, compact disc ii ACKNOWLEDGEMENTS It is a pleasure to thank those who supported me making this thesis possible. I am thankful to my supervisor, Hazem Al-Bermanei, whose intricate know- ledge of coding theory inspired me, and whose lectures, encouragement, and support enabled me to develop an understanding of this subject.
    [Show full text]
  • Network Coding for Error Correction
    Network Coding for Error Correction Thesis by Svitlana S. Vyetrenko [email protected] In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2011 (Defended May 26, 2011) 1 To my parents 2 Acknowledgements I would like to thank my advisor Tracey Ho for all her help and encouragement; Michelle Effros for her valuable suggestions; my thesis committee members Joel Tropp and Houman Owhadi for their helpful feedback on my work; Sidharth Jaggi for being a great host and sharing his enthusiasm about research; Theodoros Dikaliotis for being my best friend throughout Caltech; Derek Leong for interesting discussions and technical assistance; my family and Stanimir Kondov for their unconditional love and support. 3 Abstract In this thesis, network error correction is considered from both theoretical and practical viewpoints. Theoretical parameters such as network structure and type of connection (mul- ticast vs. nonmulticast) have a profound effect on network error correction capability. This work is also dictated by the practical network issues that arise in wireless ad-hoc net- works, networks with limited computational power (e.g., sensor networks) and real-time data streaming systems (e.g., video/audio conferencing or media streaming). Firstly, multicast network scenarios with probabilistic error and erasure occurrence are considered. In particular, it is shown that in networks with both random packet era- sures and errors, increasing the relative occurrence of erasures compared to errors favors network coding over forwarding at network nodes, and vice versa. Also, fountain-like error- correcting codes, for which redundancy is incrementally added until decoding succeeds, are constructed.
    [Show full text]