Low Latency and Low Complexity Communication on High Noise Channels
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Low Latency and Low Complexity Communication on High Noise Channels

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Low latency and low power communications have broad applications such as Internet of things (IoT), autonomous vehicles, industry automation (collaborative robots), health procedures (like robot assisted surgery requiring haptic feedback), satellite communication, radar applications, virtual reality headsets and millimeter Waves (mmWave).Low latency communications is in high demand for autonomous systems to be able to react swiftly to changes in the environment and to unexpected situations. Latency is tied to the technology used and even more to the overall architecture adopted. Enhanced mobile broadband, massive machine type communications and ultra-reliable and low latency communication are the most prominent promises of 5th generation mobile network (5G). The low power wide area networks communications is expected to grow exponentially from the 1.5B\$ of 2018 to 65B\$ in 2025 and communication services, asset tracking and smart buildings (installation and operation) are just some of its applications. Low power communications can use a number of different protocols and systems like Narrow-band (NB) IoT and Long Range Wide Area Network (LoRaWAN). Long range wide area networks use unlicensed spectrum and are more suitable for applications generated in low traffic volume (which is typically the case for IoT). All these applications of low power and low latency communication were the motivation behind our research.

In this thesis, we introduce a low-rate low-density parity-check (LDPC) code for channels with extreme noise and present a low latency and low complexity communication method for low power applications. We then show that this design has the ability of outperforming uncoded modulation for the signal-to-noise ratios (SNR) above $-3$ dB per information bit and achieve a $3$ dB gain as SNR grows.We use belief propagation (BP) decoding only on information bits to decode these codes and by doing so the overall complexity of decoding would be log-linear in terms of block size. To improve code performance, information bits are further protected with a polar code. The combined design has low complexity of decoding, small latency and a vanishing bit error rate (BER).

We also prove upper and lower bounds on bit error rate of these algorithms at any SNR and study a combined scheme that splits the information block into $b$ blocks and protects each with some polar code.Decoding moves back and forth between polar and LDPC codes, every time using a polar code of a higher rate. For a sufficiently large constant $b$ and a large block size, this design yields a vanishing BER at any SNR that is arbitrarily close to the Shannon limit of -1.59 dB. This scheme also has very low complexity and decodes $m$ information bits with complexity of order $\mathcal{O}(m\log m)$ per information bit.

In the subsequent chapters of this thesis, we combine polar and low-density parity-check (LDPC) with parity checks of small weight to achieve low latency and low complexity codes for high noise channels. Decoding of this codes also performs several iterations of the belief propagation (BP) algorithm.Partially corrected bits are then passed to a short polar code that uses successive cancellation list (SCL) decoder. The newly corrected bits then serve as the new inputs for the LDPC decoder. For codes of rate less than 0.05, the algorithm performs on a par with a cyclic redundancy check (CRC) aided successive cancellation list (CA-SCL) decoder, while substantially reducing its latency.

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