Decoding of Punctured Convolutional Codes

Abstract

To achieve the specified probabilistic-temporal characteristics of adaptive communication systems, an important task is to choose the optimal signal-code construction. At the same time, for the most flexible control of the code rate and, consequently, the correcting ability of the code, the method of puncturing bits is often used. In this case, some of the encoded bits are not transmitted over the communication channel, and zero bit values are usually put in their places on the receiving side. On average, half of these zero bits will be correct, but their reliability will be minimal. The paper presents a method for reconstructing perforated bits of a precision code, i.e. their "recovery with some probability". It is shown that if one of the connected bits is punctured, then it can be reconstructed. An assessment of the reliability of the reconstructed bit can also be obtained. The purpose of the work is to demonstrate the possibility of reconstructing the perforated bits of the convolutional code and obtaining their soft evaluation, as well as the probabilistic characteristics provided by this method. The purpose of the punctured bit reconstruction method is to improve the probabilistic characteristics of adaptive packet data communication systems using perforated convolutional codes. Research methods: as a research method, a simulation of a communication system using punctured convolutional codes with various perforation masks was carried out. As a result , expressions for the relationship of encoded bits of a convolutional code with a code rate of 1/2 for any polynomials are obtained. Expressions are used to obtain the reconstructed bit and evaluate its reliability. Theoretical expressions are given for the probability of occurrence of a given number of errors for a channel with an additive white Gaussian noise. The novelty lies in the theoretical elaboration of a method for reconstructing and evaluating the reliability of punctured bits of convolutional codes. The practical significance lies in improving the probabilistic characteristics of adaptive communication systems that use perforated convolutional codes, namely, in reducing the bit-error rate and packet error rate.