Channel Coding Parameter Analysis Under Low Signal-to-noise Ratios

The parameter analysis technology for channel coding uses the received coded sequences torecognize the coding parameters for the purpose of retrieving information, in situations wherethose parameters are not known to the receiver. Such technology is essential in applications likecognitive radio and signal interception. Development of new communication schemes and signalprocessing techniques keeps lowering the necessary power for transmitting; as a result, thereceived signal is becoming weaker than ever before. For these reasons, the thesis studies on theparameter analysis problem under low signal-to-noise ratios (SNR’s).The basic principle of many methods in this field is to find out the dual code or dual spaceof a code through solving a homogeneous equation based on the check equation. Existingmethods usually use hard decision sequences of the demodulator. Thus, these methods have thefatal defect of insufficient error-tolerating capability in low SNR cases. So, the thesis proposes anovel idea that the soft-decision sequences should be used for solving the equation model, andthe probability that the equation holds right should be regarded as the measurement of theperformance of a solution vector. Moreover, a practical computational method which reduces thecomplexity is developed. Simulation results show that, compared with the classic algorithmbased on fast Walsh-Hadamard transform (FWHT), the new algorithm improves the recognitionperformances, especially when the SNR is low.Methods based on finding dual code by solving homogeneous equations have highcomputational and spatial complexity, and their practicality falls rapidly as the code lengthincreases. The thesis presents a new approach, which turns the recognition problem into aproblem of solving the non-homogeneous error-containing equations, for getting the generatormatrix from the code space directly. Methods based on FWHT and based on the probability thatthe equation holds right are introduced for solving the equations. Under low and mediumcode-rate conditions, the computational and spatial complexity of the new approach are bothmuch lower, and thanks to the soft-decision, the error-tolerating capability is remarkablyincreased. As for the estimation of the code length and synchronization parameter, the thesiscorrects the existing code-weight distribution distance formula and proposes the statisticalmethod for the code-weight distribution distance using soft-decision, which brings theimprovement of performances and the error-tolerating capability.Most existing methods for convolutional codes only apply to non-recursive codes, andsuffer from defects of poor recognition performances and high computational complexity. Andthe only existing method for recursive convolutional codes can not apply to non-systematiccodes. To solve this problem, the thesis proposes to use an ARMA system model to describe recursive systematic convolutional (RSC) encoders, and turn the recognition problem into aproblem of system identification. Thus, the Bayesian methods can be used for estimation ofencoder parameters. The thesis derives the conditional probability expressions of informationbits and the encoder coefficients for RSC coding, and realizes the parameter estimation of RSCcodes based on soft-decision by applying the Gibbs sampling method, which belongs to a classof Monte Carlo Bayesian methods, to the problem. By some revising and generalization, the newalgorithm can be applied to non-recursive non-systematic codes. Simulation results show that thealgorithm has good performances and moderate complexity, and moreover, the advantage that itapplies to all types of convolutional codes.For parameter analysis of convolutional codes, the thesis also proposes a method based oncost function of the encoder parameters. Firstly, starting from the description of RSC codes bygenerator polynomials, a cost function is designed with respect to the encoder coefficients.Secondly, an iterative algorithm is developed based on the optimization method, i.e. the simpleconjugate gradient algorithm. Finally, the manner of assisting a simple iterative process by atry-again scheme is proposed to improve the probability of correct convergence. Furthermore,this algorithm has also good adaptability and can also be applied to non-recursive non-systematiccodes after some generalization. Simulation results and analysis show that this algorithmrecognizes correct parameters of convolutional encoders efficiently with low computationalcomplexity, under low SNR conditions.