A polar codes-based distributed UEP scheme for the internet of things

The Internet of Things (IoT), which is expected to support a massive number of devices, is a promising communication scenario. Usually, the data of different devices has different reliability requirements. Channel codes with the unequal error protection (UEP) property are rather appealing for such applications. Due to the power-constrained characteristic of the IoT services, most of the data has short packets; therefore, channel codes are of short lengths. Consequently, how to transmit such nonuniform data from multisources efficiently and reliably becomes an issue be solved urgently. To address this issue, in this paper, a distributed coding scheme based on polar codes which can provide UEP property is proposed. The distributed polar codes are realized by the groundbreaking combination method of noisy coded bits. With the proposed coding scheme, the various data from multisources can be recovered with a single common decoder. Various reliability can be achieved; thus, UEP is provided. Finally, the simulation results show that the proposed coding scheme is viable

Faulty Successive Cancellation Decoding of Polar Codes for the Binary Erasure Channel

In this paper, faulty successive cancellation decoding of polar codes for the binary erasure channel is studied. To this end, a simple erasure-based fault model is introduced to represent errors in the decoder and it is shown that, under this model, polarization does not happen, meaning that fully reliable communication is not possible at any rate. Furthermore, a lower bound on the frame error rate of polar codes under faulty SC decoding is provided, which is then used, along with a well-known upper bound, in order to choose a blocklength that minimizes the erasure probability under faulty decoding. Finally, an unequal error protection scheme that can re-enable asymptotically erasure-free transmission at a small rate loss and by protecting only a constant fraction of the decoder is proposed. The same scheme is also shown to significantly improve the finite-length performance of the faulty successive cancellation decoder by protecting as little as 1.5% of the decoder.Comment: Accepted for publications in the IEEE Transactions on Communication

On the Construction and Decoding of Concatenated Polar Codes

A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any $\epsilon > 0$, and total frame length $N$, the parameters of the scheme can be set such that the frame error probability is less than $2^{-N^{1-\epsilon}}$, while the scheme is still capacity achieving. This improves upon 2^{-N^{0.5-\eps}}, the frame error probability of Arikan's polar codes. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity

Optimization and Applications of Modern Wireless Networks and Symmetry

Due to the future demands of wireless communications, this book focuses on channel coding, multi-access, network protocol, and the related techniques for IoT/5G. Channel coding is widely used to enhance reliability and spectral efficiency. In particular, low-density parity check (LDPC) codes and polar codes are optimized for next wireless standard. Moreover, advanced network protocol is developed to improve wireless throughput. This invokes a great deal of attention on modern communications

A Non-Asymptotic Approach to the Analysis of Communication Networks: From Error Correcting Codes to Network Properties

This dissertation has its focus on two different topics: 1. non-asymptotic analysis of polar codes as a new paradigm in error correcting codes with very promising features, and 2. network properties for wireless networks of practical size. In its first part, we investigate properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief propagation (BP) as the decoding method. We provide a stopping set analysis for the factor graph of polar codes, where we find the size of the minimum stopping set. Our analysis along with bit error rate (BER) simulations demonstrates that finite-length polar codes show superior error floor performance compared to the conventional capacity-approaching coding techniques. Motivated by good error floor performance, we introduce a modified version of BP decoding while employing a guessing algorithm to improve the BER performance. Each application may impose its own requirements on the code design. To be able to take full advantage of polar codes in practice, a fundamental question is which practical requirements are best served by polar codes. For example, we will see that polar codes are inherently well-suited for rate-compatible applications and they can provably achieve the capacity of time-varying channels with a simple rate-compatible design. This is in contrast to LDPC codes for which no provably universally capacity-achieving design is known except for the case of the erasure channel. This dissertation investigates different approaches to applications such as UEP, rate-compatible coding, and code design over parallel sub-channels (non-uniform error correction). Furthermore, we consider the idea of combining polar codes with other coding schemes, in order to take advantage of polar codes\u27 best properties while avoiding their shortcomings. Particularly, we propose, and then analyze, a polar code-based concatenated scheme to be used in Optical Transport Networks (OTNs) as a potential real-world application The second part of the dissertation is devoted to the analysis of finite wireless networks as a fundamental problem in the area of wireless networking. We refer to networks as being finite when the number of nodes is less than a few hundred. Today, due to the vast amount of literature on large-scale wireless networks, we have a fair understanding of the asymptotic behavior of such networks. However, in real world we have to face finite networks for which the asymptotic results cease to be valid. Here we study a model of wireless networks, represented by random geometric graphs. In order to address a wide class of the network\u27s properties, we study the threshold phenomena. Being extensively studied in the asymptotic case, the threshold phenomena occurs when a graph theoretic property (such as connectivity) of the network experiences rapid changes over a specific interval of the underlying parameter. Here, we find an upper bound for the threshold width of finite line networks represented by random geometric graphs. These bounds hold for all monotone properties of such networks. We then turn our attention to an important non-monotone characteristic of line networks which is the Medium Access (MAC) layer capacity, defined as the maximum number of possible concurrent transmissions. Towards this goal, we provide a linear time algorithm which finds a maximal set of concurrent non-interfering transmissions and further derive lower and upper bounds for the cardinality of the set. Using simulations, we show that these bounds serve as reasonable estimates for the actual value of the MAC-layer capacity

Approximate quantum error correction for generalized amplitude damping errors

We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes. The performance of such error-correcting schemes is quantified by means of the entanglement fidelity as a function of the damping probability and the non-zero environmental temperature. The recovery scheme employed throughout our work applies, in principle, to arbitrary quantum codes and is the analogue of the perfect Knill-Laflamme recovery scheme adapted to the approximate quantum error correction framework for the GAD error model. We also analytically recover and/or clarify some previously known numerical results in the limiting case of vanishing temperature of the environment, the well-known traditional amplitude damping channel. In addition, our study suggests that degenerate stabilizer codes and self-complementary nonadditive codes are especially suitable for the error correction of the GAD noise model. Finally, comparing the properly normalized entanglement fidelities of the best performant stabilizer and nonadditive codes characterized by the same length, we show that nonadditive codes outperform stabilizer codes not only in terms of encoded dimension but also in terms of entanglement fidelity.Comment: 44 pages, 8 figures, improved v

Mapping Design for 2M -Ary Bit-Interleaved Polar Coded Modulation

This paper proposes a mapping design for bit-interleaved polar coded modulation (BIPCM) systems with belief propagation (BP) decoding. We first introduce a two-layer bipartite graph to represent BIPCM, where a new mapping graph linking polar graph to modulator is added to the conventional factor graph. Then, a mapping design is proposed and the design paradigm is to separate sub-channels with lower reliability to different stopping trees of polar codes, aiming to make sure that each stopping tree receives reliable extrinsic information from demodulator. The proposed mapping algorithm is employed for BIPCM with traditional polar codes over 16-quadrature amplitude modulation (QAM) and 256-QAM. Numerical results show that our scheme can improve the error-correcting performance compared to the conventional scheme with a random mapping. Furthermore, to meet code-length requirement of different modulation orders, we propose an efficient method to construct flexible-length polar code (FLPC) by coupling several short length polar codes with a repeat-accumulate (RA) code. Also, the proposed FLPC is employed in the BIPCM system, with the designed mapping algorithm, simulation result also reveals that the block error rate performance of proposed BIPCM scheme with BP decoding outperforms the one with successive cancellation decoding by providing a gain up to 1 dB