Seung-Chan Lim

Design of Length-Compatible Polar Codes Based on the Reduction of Polarizing Matrices

Length-compatible polar codes are a class of polar codes which can support a wide range of lengths with a single pair of encoder and decoder. In this paper we propose a method to construct length-compatible polar codes by employing the reduction of the 2n × 2n polarizing matrix proposed by Arikan. The conditions under which a reduced matrix becomes a polarizing matrix supporting a polar code of a given length are first analyzed. Based on these conditions, length-compatible polar codes are constructed in a suboptimal way by codeword-puncturing and information-refreezing processes. They have low encoding and decoding complexity since they can be encoded and decoded in a similar way as a polar code of length 2n. Numerical results show that length-compatible polar codes designed by the proposed method provide a performance gain of about 1.0 - 5.0 dB over those obtained by random puncturing when successive cancellation decoding is employed.

Mapping Selection and Code Construction for 2^m-ary Polar-Coded Modulation

This paper proposes a mapping strategy and a code construction method for 2m-ary polar-coded modulation. In order to find a good mapping for a polar code in an efficient way, we reduce a search space for mapping patterns by exploiting the properties of its polarizing matrix. Once a mapping is selected, the set of unfrozen information bits to define a polar code is automatically determined. Numerical results show that our approach can provide a performance gain of about 0.3-0.5 dB over a conventional approach using random mapping and the polar code optimized for binary phase-shift keying (BPSK) modulation, when pulse-amplitude modulation (PAM) with Gray labelling is employed.

Blind Compensation for Phase Noise in OFDM Systems over Constant Modulus Modulation

A blind algorithm is proposed in order to compensate for the phase noise resulting from imperfect oscillators in orthogonal frequency-division multiplexing (OFDM) systems over constant modulus modulation. In the proposed algorithm, one received OFDM symbol is partitioned into subblocks in the time domain and the phase noise over each subblock is approximated as its time-average. Under the approximation, the squared magnitude of the channel gain multiplied by the data symbol at each subcarrier is shown to be expressed in terms of these time-averages and the discrete Fourier transform (DFT) coefficients of the received samples at each subblock with zero padding. Based on the relation, the proposed algorithm compensates for the phase noise without pilot symbols. Numerical results show that the proposed algorithm outperforms conventional algorithms as well as it requires lower computational complexity.