It is widely acknowledged in communication theory that polar codes have been proven to achieve channel capacity across a range of communication channels. However, their exceptional performance is usually evaluated through simulations or analyses conducted under the assumption of infinite precision, i.e., floating-point arithmetic, which represents an ideal numerical computation. To address this implementation challenge, this work proposes a min-sum successive cancellation (MS-SC) polar decoder employing all-integer quantization to improve practicality in real-world scenarios. To balance the trade-off between practicality and decoding performance, we investigate whether 5-bit all-integer quantization is the optimal choice for the MS-SC polar decoder. Moreover, the simulation results over fading channels show that the proposed decoder achieves a performance almost equivalent to the high-precision successive cancellation (SC) decoder. The integer-based calculation for the MS-SC polar decoder reduces computational complexity by $75\%$ compared to the conventional SC decoding algorithm with infinite-precision computation.

The theoretic results of MIMO capacity tell us that the higher the number of antennas are employed, the higher the transmission rate is. This makes MIMO systems with hundreds of antennas very attractive but one of the major problems that obstructs such large dimensional MIMO systems from the practical realization is a high complexity of the MIMO detector. We present in this paper the new soft output MIMO detector based on matched filtering that can be applied to the large MIMO systems which are coded by the powerful non-binary LDPC codes. The per-bit complexity of the proposed detector is just 0.28% to that of low complexity soft output MMSE detector and scales only linearly with a number of antennas. Furthermore, the coded performances with small information length 800 bits are within 4.2 dB from the associated MIMO capacity.

In this paper, the application of non-binary low-density parity-check (NBLDPC) codes to MIMO systems which employ hundreds of antennas at both the transmitter and the receiver has been proposed. Together with the well-known low-complexity MMSE detection, the moderate length NBLDPC codes can operate closer to the MIMO capacity, e.g., capacity-gap about 3.5 dB (the best known gap is more than 7 dB). To further reduce the complexity of MMSE detection, a novel soft output detection that can provide an excellent coded performance in low SNR region with 99% complexity reduction is also proposed. The asymptotic performance is analysed by using the Monte Carlo density evolution. It is found that the NBLDPC codes can operate within 1.6 dB from the MIMO capacity. Furthermore, the merit of using the NBLDPC codes in large MIMO systems with the presence of imperfect channel estimation and spatial fading correlation which are both the realistic scenarios for large MIMO systems is also pointed out.