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A Class Project on an LDPC-Based Error Correcting System

ABSTRACT

The low-density parity check (LDPC) code is an error correcting code that closely approaches the information theoretical channel limit, also called channel capacity. LDPC and Turbo codes are the only two currently known codes that are denominated capacity approaching codes, and are extensively used in communication systems requiring high capacity. It was only after several decades of research, sprung from Claude Shannon’s seminal work on the mathematics of communication theory, that a capacity approaching code was designed. Developing a capacity approaching code requires the knowledge of a large variety of different error correcting approaches, generally based on advanced mathematic skills. This knowledge typically is taught in classes dealing with coding theory, error correction codes, or information theory etc. Hence, LDPC codes are seldom taught in an undergraduate curriculum, as they are combined in graduate programs with other coding techniques. However, it has been recently found that LDPC code can be understood from factor graphs, which is a dramatically different approach as that used traditionally in coding theory classes. With the factor graph approach, it is possible for undergraduate students to have an introductory experience to error correcting codes in the LDPC family. This paper documents the findings resulting from a project done in a senior-level Digital Signal Processing (DSP) class. The successful class project proves that it is possible for undergraduate students to understand LDPC codes based on factor graphs, without any other traditional coding theory background.

I. INTRODUCTION

Our lives are a daily succession of conscious information exchanges. We talk to people, listen to the radio, watch TV, browse the Internet, make phone calls, check the stock market with our cell- phones, send text messages, etc. Some information exchange is done without us even realizing it. We swipe our debit card to buy an espresso and a connection is immediately made to transfer the funds from our bank account to that of the vendor. We approach a grocery store entrance and a signal is sent that opens the door automatically. Our cell-phones are constantly sending location information so that we can be located immediately, if needed. We enter a bank and a closed circuit television system is alerted to begin recording a security video. Most of these examples include some form of electronic communication technology. The amazing rate at which information availability is increasing has also increased the number of Internet users to over 1.5 billion people, a 225% increase since the peak of the dot com boom in the year 2000 [1]. Another electronic communication technology whose use has increased significantly in the last few years is mobile-phones. Over 2.4 billion people use cell-phones [2]. Third-world countries show the largest increase in cell-phone usage, since no tangible channel (i.e. copper lines, optical fiber, microwaves, etc.) is needed (other than ubiquitous towers) to enable communication. Although a plateau has not been reached yet, further increases in availability of Internet and cell-

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Koh, M., & Rodriguez-Marek, E., & Talarico, C., & Freiberger, D. (2008, June), A Class Project On An Ldpc Based Error Correcting System Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--3504