Trellis-Coded Modulation Course Project - Google Sites

March 14, 2005

Brian K. Butler

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UCSD ECE 259BN Trellis-Coded Modulation Course . . Project . . . . . Topics on the weight distribution of error correcting codes.

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Trellis-Coded Modulation Course Project Topics on the weight distribution of error correcting codes. Abstract This project report covers several areas that I found interesting. First, for reference sake, I plot the performance bounds of convolutional codes for rates 1/2, 1/3, and 1/4. Secondly, I explore some of the details of computing the weight spectra of convolutional codes with several examples, and begin the process of finding good codes. Finally, I take a very quick look at the rate = 1/3 repeat accumulate code.

Table of Contents Abstract

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Table of Contents

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1. BER performance of convolutional codes

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2. Computation of the Weight Spectrum

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3. Eliminating Catastrophic Codes

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4. Weight Spectrum examples

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5. Repeat Accumulate Code

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References

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Appendix A – ‘wtspec’ source code

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Appendix B – ‘iscatas’ source code

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1. BER performance of convolutional codes The bounds used To provide a reference for further discussions in the report, I first compute the BER upper bounds for nearly all of the “Noncatastrophic” convolutional codes presented in (Larsen, 1973). These are all defined as polynomial generators. Larsen presents the encoders that generate maximal free distance codes for rates of 1/2, 1/3, and 1/4. He does this for constraint lengths from m equal 2 to 13. (Larsen uses the ν=m+1 for constraint length that describes a code with 2m states). I’ve only left out m = 13 from my figures in the interest of time. I have used the tightest union upper bound presented class, and also found in (§12.2 of Lin & Costello, 2004 and §6.2 of Schlegel & Perez, 2004) before approximations are made.

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