DOCSLIB.ORG

Design and Implementation of an Improved Error Correcting Code for 5G Communication System

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Design and Implementation of an Improved Error Correcting Code for 5G Communication System Journal of Communications Vol. 14, No. 2, February 2019 Design and Implementation of an Improved Error Correcting Code for 5G Communication System Bashar M. Mansoor and Tarik Z. Ismaeel 1Department of Electrical Engineering, College of Engineering, University of Baghdad, Iraq 2Department of Electronic & Communication Engineering, College of Engineering, University of Baghdad, Iraq Email: [email protected]; [email protected] Abstract—Channel coding, which means adding a redundancy step toward very high throughput wireless systems [5]. to information in order to minimize a bit error rate is one of Recently, a lot of research has confirmed that LDPC key technologies in development of each generation of mobile codes achieve decoding with better bit error rate (BER) systems. Recently, Low-Density Parity-Check (LDPC) Code has been selected to provide channel coding for 5G performance and lower computational complexity than communication systems due to its high performance that turbo codes that are used in 3G and 4G systems; approaches closely Shannon's limit, and its low complexity. however, other features such as decoder flexibility and However, there is still some work that is related to throughput, interconnection complexity still need to be improved. flexibility, and complexity of LDPC codes needs to be LDPC codes have become a key component of many considered to meet all the 5G requirements. In this paper, an communication systems such as WiFi (IEEE802.11n), improved code of high throughput and flexibility was proposed. Here, a code is flexible if it supports a large number of coding WiMAX (IEEE802.16e), DVB-S2, CCSDS, and ITU rates and block lengths. In addition, the proposed code can be G.hn [6]. The LDPC codes used in WiMAX standards encoded and decoded with low computational and are designed under hardware constraints; however, implementation complexities. The encoder and decoder can be providing LDPC codes that have different lengths and implemented based on IEEE WiMAX standards, so the rates imposes significant challenges on the LDPC generated codes can be compared to the standard WiMAX decoder realization [5]. To overcome the problems of LDPC codes. Theoretical calculations show that the proposed codes achieve significant improvements in throughput, latency, implementation and to meet the channel code and computational and implementation complexity. The requirements of 5G, several parameters such as simulation employed WiMAX 802.16e standard and a fixed throughput, flexibility, and complexity need to be clock frequency of 500 MHz. The throughput ranged from 372 improved. In this paper, two architectures for encoder Mbps for rate 1/2 codes to 915 Mbps for rate 5/6 codes. An and decoder are proposed based on WiMAX 802.16e increasing of 1.4–2.2 times was obtained compared to the standard to provide codes with high flexibility, improved standard LDPC codes. throughput, and low complexity. The paper is organized Index Terms—5G channel coding, WiMAX LDPC code, code as follows; Section II: introduces standard LDPC code. flexibility, throughput, latency, computational and Section III: shows an overview on turbo code. The implementation complexity, BER performance. model proposed is depicted in section IV. Section V shows the valuation of the proposed code, while the I. INTRODUCTION simulation results with their discussions are detailed in The recent interest in channel coding of 5G Section VI. Finally, Section VII documents some communication systems has directed to the Low-Density conclusions based on the results of this work. Parity-Check (LDPC) codes [1]. LDPC codes were invented by Gallager in 1960 and rediscovered by II. LDPC CODES MacKay and Neal in the late of 1990s [2], [3]. LDPC LDPC codes are fully characterized by a binary codes are linear block codes and defined by a binary matrix called parity-check matrix (H-matrix), and also matrix called parity-check matrix (H-matrix). They are can be represented by bipartite graphs called Tanner called low-density parity check because the density of graph in which non-zero elements (ones) of each row their non-zero elements (ones) in H-matrix is very low. and column in H-matrix are represented by two sets of Because of high performance and low complexity, nodes; check node (CN) and variable node (VN) LDPC codes have been selected to provide channel respectively. Variable and check nodes are connected by coding for the next generations of communication edge connections where the number of edges in the systems [4]. The WiMAX 802.16e standard that was graph is equal to the number of ones in H-matrix. Fig. 1 developed by IEEE uses LDPC codes as a channel shows an example of Tanner graph for H matrix given coding scheme to meet the requirements of mobile below: communication systems, where this standard is the next 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 0 퐻 = [ ] (1) Manuscript received June 2, 2018; revised January 2, 2019. 0 1 1 1 0 0 1 1 doi:10.12720/jcm.14.2.88-96 1 0 0 1 1 1 0 0 ©2019 Journal of Communications 88 Journal of Communications Vol. 14, No. 2, February 2019 All six matrices can be used when the expansion factor, Z is less than the maximum expansion (Z =96). f 0 In this case, each matrix can be expanded according to Fig. 1. Tanner graph representations of LDPC code the following equations [9] LDPC code, x must satisfy the equation below 푃 푓,푖,푗 = 푃 푖,푗 if 푃 푖,푗 ≤ 0 (4) 퐻푥푇 = 0 (푚표푑 2), ∀ 푥 ∈ 푐 (2) 푃 푓,푖,푗 = 푃 푖,푗 ∗ 푍푓/푍0 if 푃 푖,푗 ≥ 0 (5) An LDPC code of N length and K information is always represented by a parity-check matrix of size (M x The number of edges is also equal to the number of N) and code rat of K/N, where M is the number of parity ones in the binary H-matrix. The degree distribution of the variable nodes and check nodes can expressed by bits equivalent to M=N-K. The node degree is the 푚푎푥 푚푎푥 푚푎푥 number of edges on each node in the H-matrix. In 푓[푑푣 , … ,3,2] and 푔[푑푐 , 푑푐 − 1] respectively [5]. addition, it represents the number of connections The six H-matrix classes of WiMAX 802.16e with its between VN and CN and defines two types of LDPC their degree distributions for VNs and CNs are summarized in Table I. codes. If the weight distribution of column weights (dv) and weight distribution of rows (dc) are constant, the TABLE I: DEGREE DISTRIBUTIONS OF THE WIMAX 802.16E LDPC code is regular LDPC code. otherwise the code is CODE irregular LDPC code. Each LDPC code that is used in WiMAX standards is defined by a sparse H-matrix which is, in turn, expanded from base matrix (Hb-matrix) of size mb x nb, where mb=M/mf and nb=N/nb with expansion factor Zf. H-matrices of WiMAX standards can be found using the following equation 푃 1,1 푃 1,2 … 푃 1,푛푏 푃 푃 … 푃 The two functions, f and g also give the fraction of H = [ 2,1 2,2 2,푛푏 ] (3) … … … … VNs and CNs with a certain degree. At the decoder, 푃 푚푏,1 푃 푚푏,2 … 푃 푚푏,푛푏 many decoding algorithms are known to recover where 푃 is circularly right-shifted identity matrix information [12]: 1) Sum-Product algorithm (SPA), 2) 푖,푗 Min-Sum algorithm, 3) Min-Max algorithm, 4) (permutation matrix) of size Z x Z . For WiMAX f f Message-Passing algorithm and 5) Bit-Flipping 802.16e, the expansion factor Zf varies from 24 to 96 with a granularity of 4 leading to support 19 different Decoding algorithm. The SPA is based on belief propagation and provides a better performance compared code sizes. The two parameters nb and mb take constant and maximum values of 24 and 12 respectively. Since to the other algorithms. It has a scheduling of two phases, permutation matrix tends to be rather large, the H-matrix therefor all VNs ae updated in phase 1 and all CNs are can be written in a smaller form. This can be updated in phase 2. In each phase, individual nodes are accomplished by labeling the circular identity matrix by parallelized, so that they are independently processed. the number of shift the matrix contained. Currently, Each VN of degree dv determines an update of message there are six different codes with four different code m by the following relation, where each message update rates that are used in WiMAX 802.16e standard based on is a Log-Likelihood Ratio (LLR). six classes of base matrix (1/2, 2/3(A, B), 3/4(A, B), 5/6) 푑푣−1 표푙푑 [7, 8]. For an expansion factor of 96 and a code rate of 휆푘 = 휆푐ℎ + ∑푙=0 휆푙 − 휆푘 (6) 1/2, the code length is 2304 and the number of parity bits where 휆 is LLR of a corresponding channel that is is 576. For the same expansion factor and code rate of 푐ℎ represented in the variable node and 휆 corresponds to 5/6, the code length is 2304 while the number of parity 푙 LLRs of the incident edges. In this paper, all simulation bits is 384. The following matrices are the H-matrices corresponding to 1/2 and 5/6 code rates. results are obtained using the Sum-Product algorithm. III. AN OVERVIEW ON TURBO CODE Turbo codes are the best available error correction technique in the last few years. They have been standardized in 3G and 4G standards because they can achieve a performance near Shannon limit [10], [11].
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]
  • 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.
    [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]