Successive Cancellation Ordered Search Decoding of Modified GN\boldsymbol{G}_N-Coset Codes

A tree search algorithm called successive cancellation ordered search (SCOS) is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding with an adaptive complexity for transmission over binary-input AWGN channels. Unlike bit-flip decoders, no outer code is needed to terminate decoding; therefore, SCOS also applies to $\boldsymbol{G}_N$-coset codes modified with dynamic frozen bits. The average complexity is close to that of successive cancellation (SC) decoding at practical frame error rates (FERs) for codes with wide ranges of rate and lengths up to $512$ bits, which perform within $0.25$ dB or less from the random coding union bound and outperform Reed--Muller codes under ML decoding by up to $0.5$ dB. Simulations illustrate simultaneous gains for SCOS over SC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the average complexity at various SNR regimes. SCOS is further extended by forcing it to look for candidates satisfying a threshold on the likelihood, thereby outperforming basic SCOS under complexity constraints. The modified SCOS enables strong error-detection capability without the need for an outer code. In particular, the $(128, 64)$ PAC code under modified SCOS provides gains in overall and undetected FER compared to CRC-aided polar codes under SCL/dynamic SC flip decoding at high SNR.Comment: 14 pages, 9 figures, 3 tables. Submitted to IEEE journal. The revised version of the first submission. Major changes: 1) No dedicated section for numerical results. Instead, simulations are provided right after the relevant section. 2) More simulation results are added to compare all the state of art polar decoders in terms of the number of arithmetic operations. arXiv admin note: text overlap with arXiv:2105.0404

Quantized Guessing Random Additive Noise Decoding

We introduce a soft-detection variant of Guessing Random Additive Noise Decoding (GRAND) called Quantized GRAND (QGRAND) that can efficiently decode any moderate redundancy block-code of any length in an algorithm that is suitable for highly parallelized implementation in hardware. QGRAND can avail of any level of quantized soft information, is established to be almost capacity achieving, and is shown to provide near maximum likelihood decoding performance when provided with five or more bits of soft information per received bit

Comparative Study of Structural and Electronic Properties of Cu-based Multinary Semiconductors

We present a systematic and comparative study of the structural and electronic properties of Cu-based ternary and quaternary semiconductors using first-principles electronic structure approaches. The important role that Cu d electrons play in determining their properties is illustrated by comparing results calculated with different exchange correlation energy functionals. We show that systematic improvement of the calculated anion displacement can be achieved by using the Heyd-Scuseria-Ernzerhof (HSE06) functional compared with the Perdew-Burke-Ernzerhof (PBE) functional. Quasiparticle band structures are then calculated within the G0W0 approximation using the crystal structures optimized within the HSE06 functional and starting from the PBE+U mean-field solution. Both the calculated quasiparticle band gaps and their systematic variation with chemical constituents agree very well with experiments. We also predict that the quasiparticle band gaps of the prototypical semiconductor Cu2ZnSnS4 in the kesterite (KS) phase is 1.65 eV and that of the stannite (ST) phase is 1.40 eV. These results are also consistent with available experimental values which vary from 1.45 to 1.6 eV.Comment: 21 pages, 8 figures, 2 table

Code-Aided Channel Estimation in LDPC-Coded MIMO Systems

For a multiple-input multiple-output (MIMO) system with unknown channel state information (CSI), a novel low-density parity check (LDPC)-coded transmission (LCT) scheme with joint pilot and data channel estimation is proposed. To fine-tune the CSI, a method based on the constraints introduced by the coded data from an LDPC code is designed such that the MIMO detector exploits the fine-tuned CSI. For reducing the computational burden, a coordinate ascent algorithm is employed along with several approximation methods, effectively reducing the required times of MIMO detection and computational complexity to achieve a satisfying performance. Simulation results utilizing WiMAX standard LDPC codes and quadrature phase-shift keying (QPSK) modulation demonstrate gains of up to 1.3 dB at a frame error rate (FER) of $10^{-4}$ compared to pilot-assisted transmission (PAT) over Rayleigh block-fading channels.Comment: This paper has been accepted by IEEE Wireless Communications Letter