This paper shows that several attractive classes of quasi-cyclic (QC) low-density parity-check (LDPC) codes can be obtained from affine planes over finite fields. One class of these consists of duals of one-generator QC codes. Here, for codes contained in this class, the exact minimum-distance and a lower bound on the multiplicity of the minimum-weight codewords are presented. It is shown that the lower bound on the multiplicity provides a very accurate indication of the bit error performance at moderate and high signal-to-noise ratios, and thus error-floor behavior can be easily predicted. Also discussed is a class consisting of codes from circulant permutation matrices. An explicit formula for the rank of the parity-check matrix is presented for these codes. Furthermore, it is shown that each of these codes can be identified as a code constructed from a constacyclic maximum distance separable (MDS) code in a similar manner to the RS-based LDPC codes presented by Chen et al. and Djurdjevic et al. Experimental results show that a number of high rate QC-LDPC codes with excellent error performance are contained in these classes.

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This paper proposes an efficient neural-network-based digital predistortion (DPD), named as envelope time-delay neural network (ETDNN) DPD. The method complies with the physical characteristics of radio-frequency (RF) power amplifiers (PAs) and uses a more compact DPD model than the conventional neural-network-based DPD. Additionally, a structured pruning technique is presented and used to reduce the computational complexity. It is shown that the resulting ETDNN obtained after applying pruning becomes so sparse that its complexity is comparable to that of conventional DPDs such as memory polynomial(MP) and generalized memory polynomial (GMP), while the degradation in performance due to the pruning is negligible. In an experiment on a 3.5-GHz GaN Doherty power amplifier (PA), our method with the proposed pruning had only one-thirtieth the computational complexity of the conventional neural-network-based DPD for the same adjacent channel leakage ratio (ACLR). Moreover, compared with memory-polynomial-based digital predistortion, our method with the proposed pruning achieved a 7-dB improvement in ACLR, despite it having lower computational complexity. INDEX TERMS digital predistortion, generalized memory polynomial, memory polynomial, neural network, pruning technique Recently, a number of neural network-based DPDs have been presented [4], [5], [8], [9]. Their accurate modeling capability of neural networks enables them to outperform Volterra-based DPDs but at the expense of computational complexity.

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