Design and Analysis of Probabilistic Shaping for Polar Coded Communication Systems with Finite Blocklength

Probabilistic shaping (PS) has been demonstrated as an efficient method to achieve the shaping gain and to approach the Shannon limit in additive white Gaussian noise channels. To narrow the shaping gap caused by the channel fluctuation and the finite blocklength, a novel PS strategy is designed for polar coded communication systems with finite blocklength in Rayleigh flat fading channels. The proposed system transmits the quadrature amplitude modulation symbols and demodulates the received signal through log-maximum-a-posteriori (Log-MAP) detection. The channel capacity is theoretically derived in terms of the mutual information considering the influence of PS and the finite blocklength. Moreover, to solve the non-convex problem that maximizes the channel capacity on the basis of mutual information, an alternating optimization algorithm is proposed. Finally, numerical results indicate that with the optimal probabilistic shaping scheme, the system has 1.7 dB and 0.45 dB gain on the block error rate and channel capacity of the uniform distribution, respectively.