Efficient Polar Code Construction for Higher-Order Modulation

Abstract

Abstract-An efficient algorithm for the construction of polar codes for higher-order modulation is presented based on information-theoretic principles. The bit reliabilities after successive demapping are estimated using the LM-rate, an achievable rate for mismatched decoding. The successive demapper bit channels are then replaced by binary input Additive White Gaussian Noise (biAWGN) surrogate channels and polar codes are constructed using the Gaussian approximation (GA). This LM-rate Demapper GA (LM-DGA) construction is used to construct polar codes for several demapping strategies proposed in literature. For all considered demappers, the LM-DGA constructed polar codes have the same performance as polar codes constructed by Monte Carlo (MC) simulation. The proposed LM-DGA construction is much faster than the MC construction. For 64-QAM, spectral efficiency 3 bits/s/Hz, and block length 1536 bits, simulation results show that LM-DGA constructed polar codes with cyclic redundancy check and successive cancellation list decoding are 1 dB more power efficient than state-of-the-art AR4JA lowdensity parity-check codes.

Polar-Coded Pulse Position Modulation for the Poisson Channel

“…The results show a slight gain in performance with respect to the state of the art transmission scheme proposed in [1]. Additionally, we demonstrated that the existing approaches of designing polar codes for the AWGN channel via biAWGN channel surrogates [6] can be extended to design polar codes on the PPM Poisson channel. We observed that the list size of the dynamic successive cancellation list decoder has an impact on the performance of the scheme.…”

“…To refer to a label at a generic time instance we drop the subscript i and write b = b 1 · · · b m [6]. The input x i to the PPM Poisson channel is the output of the PPM mapper defined as…”

“…To calculate the J function and its inverse J −1 , we use the approximation 3) MI Demapper Gaussian Approximation Construction: For the proposed scheme, we use the construction approach from [6] called MI demapper GA (MI-DGA). The idea is to first characterize the bit-channels at the output of the PPM demappers by mutual information expressions that take into account the dependence of the soft information produced by the PPM demappers on all the previous detected bits.…”

Successive Cancellation List Decoding of BMERA Codes with Application to Higher-Order Modulation

“…3 shows the performance of 64-QAM polar and BMERA codes with n = 256 QAM symbols per block and a spectral efficiency of 3 bits per channel use over the AWGN channel. All codes are optimized for a SNR of E s /N 0 = 11 dB using the methods of [11] with set partitioning label. The comparison shows a similar result as in the BPSK case.…”

Flexible IR-HARQ scheme for polar-coded modulation

“…Polar-coded modulation (PCM) is discussed in [5]- [7]. The performance comparison and efficient code design methods of three polar-coded modulation schemes are presented in [8,Fig. 11].…”