Efficient implementation of Gaussian elimination method to recover generator polynomials of convolutional codes

Abstract

One of the most important objectives in wireless communication is to transmit the information free of errors and to detect the data correctly. With a view to avoid occurrence of errors in communication channel, error correction techniques, also called channel coding, are used. Convolution encoding technique is the forerunner amongst those employed. In wireless communication systems, signal strength decreases logarithmically and results in fading. This fading causes random errors or burst errors (in case of deep fades). The burst errors are converted to random errors by interleaving techniques and then channel coding is used to combat the random errors. In convolutional codes, information bits are encoded by using primitive polynomials implemented in the form of shift registers. In this paper a method is proposed to detect the generator polynomial and the code rate of the convolution encoded data, once received. The information is encoded by Convolution (n, k, m) codes and then its generator polynomial is detected by using the Gaussian Elimination Method. Here n shows the data bit (parity and information), k represents the information bits and m shows the length of the registers. In Gaussian elimination method the variables are removed step by step. This elimination is different from the normal one in a sense that it is implemented over GF (2). This detection algorithm can be utilized efficiently to match convolutionally encoded reference stream to the one generated by above-mentioned convolutional encoder. This can also be utilized to verify the generator polynomial of the encoded output stream before feeding it to the complex decoder to avoid time-consuming and exhaustive debugging.