Polar Codes for Informed Receivers

Abstract

The problem of sending independent messages to a receiver which already has been informed a subset of messages as side information is studied. Which messages are available at the receiver is assumed to be oblivious to the transmitter. A simple yet powerful construction of codes for informed receivers based on polar codes is proposed to efficiently and fairly convert side information into reduction in probability of errors for any message side information. Compared with existing designs based on codes on graph or algebraic codes, the proposed construction is both conceptually and practically simple. Moreover, the codes inherit many good properties of polar codes, including explicit construction and low-complexity encoding and decoding scaling such as $\mathcal {O}(N\log N)$ where $N$ is the blocklength. Extensions to high-order modulation and block fading channels are also proposed. Simulation results indicate that for every side information configuration, the proposed codes can convert side information into reduction in signal-to-noise ratio of roughly 6 dB/bit at bit error rate of 10−5 under additive white Gaussian noise channel or block fading channel.