Standard Coding Theory Project Report

1503 Words May 15th, 2015 7 Pages
EE – 653 CODING THEORY PROJECT REPORT

REDUCING THE GAP TO CAPACITY OF A RATE 1/3 CODE VIA CONVOLUTIONAL ENCODING/DECODING

ARUN PRAKASH NACHIMUTHU
MARIA HASHMI

ABSTRACT
In this project we are trying to minimize the gap-to capacity of a channel given by Shannon’s theoretical limit of a rate 1/3 code. This is done through a convolutional encoding/decoding by varying memory elements for both soft and hard decision decoding. The basic concepts associated with the convolution code with its encoding and decoding schemes are used in this project. Using Shannon’s optimal code we compare the gap to capacity of the algorithm that is implemented. Finally we show that the gap – to capacity can be minimized with respect to the sub optimal un-coded code word or a 1/3 repetition code.
INTRODUCTION
For a given code rate constraint of R= 1/3, a binary input AWGN channel this project presents various convolutional decoder and encoder of varying memory element sizes to reduce the gap to capacity of a code with respect to Shannon’s limit.
SHANONS CAPACITY THEOREM AND CHANNEL CODING
Despite the presence of noise, the error performance of a data communication system can be decreased to an arbitrarily low error rate, so long as the data rate was below a certain level (i.e.) the presence of noise limits the data rate not the error rate.
• To improve the error performance of communication system requires larger Bandwidth.
• If we are willing to accept erroneous data, the capacity of any…
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