Research On Estimation Of Error Probability Via Radius Of Decision Region

Decoding error probability is one of the fundamental problems in the communication theory and practice. The main methods to estimate the error rate include Monte Carlo simulation, important sampling method, and the bound of error rate, and so on. In these methods, Monte Carlo simulation requires excessive computation for Turbo-like long codes, the application of important sampling method is limited, and bounding techniques, most based on maximum likelihood decoding assumption, are generally relatively loose. Due to the fact that all the problems of decoding error probability are decided by decision regions of codewords, an idea to research on error probability from the geometry characteristic of decision regions is conceived.This thesis focuses on estimating decoding error rate via radius of decision region, and the main contributions include:1. In more general cases, the definition of radius of decision region is given and the relation between distribution of radius of decision region and error probability is deduced. On account of the open decision region for most codewords, the probability density function (PDF) of radius of decision region actually does not exist. We put forward to describe the error probability by using the cumulative distribution of radius of decision region, and validate the relation between radius of decision region and error probability in many cases, such as high order modulation, short codes, Turbo codes, low-density parity-check (LDPC) codes, and so on.2. An improved approximation for word error rate (WER) of Turbo-like codes is proposed. This formula can simply be expressed in the form of Gaussian Q-function, which includes signal-to-noise ratio, mathematical expectation and variance on squared radius of decision region, etc. Simulation results show that in additive white Gaussian noise channels, when the error rate is higher than the error floor, the maximum deviation of the approximation and Monte Carlo values can be reduced to0.05dB; while in typical fading channels such as Rician, Nakagami channels, the error between the proposed formula and Monte Carlo simulation is no more than0.5dB.3. The impact of statistical error on the proposed formula of WER for Turbo-like codes is investigated, which is caused by using the sample mean and variance to replace mathematical expectation and variance of radius of decision region. Because the two parameters about the radius of decision region are obtained by the simulation measurement, their statistical error may affect the accuracy of the proposed formula. Theoretical and simulation results show that, when the number of radiuses of decision region is about the order of102, the error between the proposed formula and Monte Carlo simulation is within0.05dB.4. The radius of decision region in hybrid automatic request retransmission is investigated, and the corresponding method to estimate error probability by using radius of decision region is put forward. We model the PDF of squared radiuses in the two regions as the joint Gaussian distribution, and then statistic the mean, variance and correlation coefficient of them, which finally can be applied to calculate the residual decoding error probability. Simulation results show that the maximum deviation between the proposed method and Monte Carlo results is no more than0.06dB.5. An improved decoding algorithm of forced convergence for LDPC coded modulation is proposed, which can reduce the decoding complexity by deleting the early convergent bits from Tanner graph. On the other hand, these convergence bits also can be deleted from the modulation constellation, and then the information of remaining bits can be updated in the smaller constellation, which may finally enhance the decoding performance. In addition, we can evaluate the decoding error probability and choose the threshold parameter by using the radius of decision region.