Achievable coding rates for AWGN and block fading channels in the finite blocklength regime

Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Faculty of Engineering, Department of Electrical and Electronics Engineering, Turkey

Approval Date: 2010




In practice, a communication system works with finite blocklength codes because of the delay constraints and the information-theoretic bounds which are proposed for finite blocklength systems can be exploited to determine the performance of a designed system. In this thesis, achievable rates for given average error probabilities are considered for finite blocklength systems. Although classical bounds can be used to upper bound the error probability, these bounds require the optimization of auxiliary variables. In this work, a bound which is called the dependence testing (DT) bound that is free of any auxiliary variables is exploited. The DT bound is evaluated by introducing a normal approximation to the information density. Simulations carried out both for the Gaussian and discrete input alphabets show the proposed approximation enables very good prediction of the achievable rates. The proposed approximation is also used to calculate the average error probability for block fading channels. Simulations performed for Rayleigh block fading channels demonstrate that the total blocklength of the system in addition to the number of fading blocks should be accounted for especially when the number of fading blocks is large. A power allocation problem in block fading channels when the channel state information is available to the transmitting side is investigated in the final part of this work. The DT bound is optimized for a given channel state vector by allocating different power levels to each fading block by exploiting short-term power allocation. A simple power allocation algorithm is proposed which comes out with very similar results compared with the analytically computed values.