Reliable Wide-Area Backscatter via Channel Polarization

Existing polar coding schemes for the two-user interference channel follow the original idea of Han and Kobayashi, in which component messages are encoded independently and then mapped by some deterministic functions (i.e., homogeneous superposition coding). In this paper, we propose a new polar coding scheme for the interference channel based on the heterogeneous superposition coding approach of Chong, Motani, and Garg. We prove that fully joint decoding (the receivers simultaneously decode both senders’ common messages and the intended sender’s private message) in the Han–Kobayashi strategy can be simplified to two types of partial-joint decoding, which are friendly to polar coding with practical decoding algorithms. The proposed coding scheme requires less auxiliary random variables and no deterministic functions and can be efficiently constructed. Furthermore, we extend this result to interference networks and show that partial-joint decoding is a general method for designing heterogeneous superposition polar coding schemes in interference networks.

Space-time block code (STBC) based on orthogonal design is one of the space-time coding methods to achieve multi-input multi-output (MIMO) diversity gain. STBC can provide sufficient space diversity gain, but it can not provide coding gain. Polar codes based on channel polarization are the first class of provably capacity-achieving codes with low encoding and decoding complexity. In order to improve the bit error rate (BER) performance of STBC, a concatenated scheme with Polar codes and STBC, named Polar-STBC scheme, is proposed in this paper. The BER performance of Polar-STBC system is discussed by numerical simulation under different polar code length, different polar code rates, and different coding methods of STBC. The results show that the performance of Polar-STBC has a big improvement in comparison with that using STBC only. The coding gain of Polar-STBC system is about 5dB when the BER is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Meanwhile, the longer code length and the lower code rate Polar codes have, the better BER performance the Polar-STBC system has. In addition, the different STBC coding methods have influence on the Polar-STBC system. The Polar-STBC system with more receiving antennas has a better BER performance in comparison with those with the same sending antennas and less receiving antennas. The coding gain of Polar-STBC system with 2 receiving antenna is 6.5dB improvement to the system with 1 receiving antenna when BER is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and the code length is 1024.

We introduce new polar coding schemes for independent non-identically distributed parallel binary discrete memoryless channels. The first scheme is developed for the case where underlying channels are time invariant (the case of a deterministic channel parameters), while the other schemes deal with a scenario where underlying channels change based on a distribution (the case of random channel parameters). For the former case, we also discuss the importance of the usage of an interleaver Q to enhance system reliability, and for the latter case, we model the channel behavior of binary erasure channels. It is shown that the proposed polar coding schemes achieve a symmetric capacity.

Polar coding is the error correction coding proposed by Arikan. In polar coding, the error rate of the decoding result differs for each bit position owing to the channel polarization. In the case of polar coding with an infinite codeword length, the decoding error rate at each position of the decoded bit sequence is polarized to 0.5 or 0. Therefore, when a codeword of a sufficient length can be adopted, information bits will be decoded without errors by placing the frozen bits to bit positions where the decoding error rates are 0.5 at the transmitter. On the other hand, in the case of polar coding with a finite codeword length, the decoding error rate at each bit position takes a value between 0.5 and 0. Therefore, the decoding errors also occur at the bit positions where the information bits are placed. In this paper, we introduce half-frozen bits into polar coding. Half-frozen bits are the information bits which play roles like frozen bits. Half-frozen bits are placed at positions where errors hardly occur within the frozen bit positions as well as where errors prone to occur within the information bit positions. As half-frozen bits, a part of information bits is used after being applied another error correction coding. This improves the decoding error rates at information bit positions which result in high decoding error rates. Therefore, half-frozen bits improve the overall bit error rate (BER) performance of polar coding. Through computer simulation, we show that the polar coding with introducing half-frozen bits provides a higher error correction performance than the original polar coding.

In this letter, a new secure information transmission scheme based on polar codes with a pre-shared secret key is proposed. In polar codes, after the channel polarization is induced, good split channels are used to transmit the user message and bad channels are utilized to support the reconstruction of the message by sharing fixed information. If the fixed information in bad channels is secret, an adversary gets difficulty in reconstructing the user message in good channels without knowledge of the fixed information. From this observation, we construct a secure information transmission scheme. By appending pre-/post-processing that imposes a dependency between the transmitted message sub-blocks, the adversary's difficulty can be changed to an intractability, since only partial information can be decodable by attackers. A new class of secret key scheme is developed in such a way.

Motivated by the capacity-approaching property of both binary polar codes (PCs) and the multi-level coding (MLC) scheme, we consider the design of modulated PC over additive white Gaussian noise (AWGN) channels. The capability of modulated PC essentially depends on the selection of information bits set from all the virtual bit channels formed by both modulation and channel polarization. To this end, we characterize the a priori distribution density as the sufficient statistic for the bit channel of individual modulation levels formed by an MLC scheme, in which the codeword of symbols is split into parallel bits streams. According to the factor graph generated by the binary PC, we apply the density evolution (DE) for each binary modulation level. Consequently, distribution densities of every bit within the modulated codeword can be obtained and we select the most reliable bits as information bits and set the complement as frozen bits. Comprehensive simulations demonstrate the validness of this approach compared to the benchmark scheme.

In this paper, we propose a reliability-based adaptive incremental redundancy hybrid automatic repeat request (IR-HARQ) scheme for rate-compatible polar codes, where the size of retransmissions is determined by the current decoding reliability. Simulation results indicate that the proposed scheme can perform better than the existing schemes based on turbo codes, low-density parity-check (LDPC) codes and raptor codes in terms of both the throughput and latency. Furthermore, with the proposed scheme, rate-compatible polar codes can achieve the performance of about 0.5 dB away from the channel capacity with the information block length of 1024 bits.

Internet of Things (IoT) and direct-access Satellite IoT (SIoT) systems demand short block-length communication to accommodate brief transmissions under strict power constraints. In this context, it is critical to ensure high error correction reliability with minimal energy. One prominent candidate for Forward Error Correction (FEC) is Polar codes. Introduced by Arikan in 2009, Polar codes achieve the capacity of binary-input discrete memoryless channels through the phenomenon of channel polarization. While generalizing Polar codes to non-binary fields <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbb{GF}(q)$</tex> can yield improved performance compared to their binary counterpart at long block lengths, they fall short at short block length even when applying techniques such as frozen-bit-pattern and kernel optimization. In this paper, additional strategies are evaluated that go beyond these baseline techniques. In detail, kernel optimization is extended towards a multi-kernel approach and a joint optimization of modulation order and code rate on system level is proposed. Simulation results demonstrate that under these careful optimizations, non-binary Polar codes can indeed outperform binary Polar codes for short block length, as well, making them the optimal channel-coding choice for SIoT applications.

With the development of flash technology, multilevel per cell (MLC) NAND flash memory has mastered the key market because of its storage capacity superiority. However, excessive density increment leads to decay of reliability of MLC NAND flash memory, thus an appropriate error correction code (ECC) is required to address this issue. This paper presents an efficient multi-strategy ECC scheme called pre-check scheme which consists of hard, quantized-soft, and pure-soft decoders geared to MLC NAND flash memory based on polar code proposed by E. Arikan to overcome the aforementioned drawbacks with better performance and lower complexity. The hard decoder is designed to correct the majority of erroneous codewords in the initial phase of the flash memory, while the soft decoders aim to correct codewords which contain larger amount of errors. In addition, we clarify that the mapping scheme using Gray code can achieve best performance compared to other alternatives.

The joint transmission scheme of polar codes and sparse code multiple access (SCMA) has been regarded as a promising technology for future wireless communication systems. However, most of the existing polar-coded SCMA (PC-SCMA) systems suffer from high latency caused by the feedback iteration and list decoding. In addition, the error performance of PC-SCMA systems is unsatisfactory for ultra-reliable transmission. Inspired by the compelling benefits of non-binary polar codes, in this paper, we design a non-binary polar-coded SCMA (NB-PC-SCMA) system with a free order matching strategy to address the issues of delay and reliability. Specifically, we first formulate a joint factor graph for NB-PC-SCMA and propose a non-binary successive cancellation list (NB-SCL) and damping based joint iterative detection and decoding (NSD-JIDD) multiuser receiver to improve the BER and latency performance. Then, a lazy-search based NB-SCL (L-NB-SCL) decoding is proposed to reduce the computational complexity by simplifying the path search pattern of the list decoder. After that, we modify the update of user nodes for SCMA detection to improve the convergence error and finally propose the improved NSD-JIDD (ISD-JIDD) algorithm, which can avoid redundant operations by exploiting L-NB-SCL decoding. Simulation results show that the proposed NB-PC-SCMA system achieves better bit error rate (BER) performance and considerable latency gain when compared to its counterparts. In particular, the proposed ISD-JIDD can achieve similar BER performance of NSD-JIDD with less complexity.

In order to address the insertion, deletion, and substitution (IDS) errors inherent in deoxyribonucleic acid (DNA) storage channels during DNA synthesis and sequencing, we propose a novel GC-balanced polar code scheme tailored to rectify these errors by incorporating the unique characteristics of the DNA storage channel into the polar code design. The innovation lies in modeling errors as a drift vector, reflecting deviations from the desired DNA sequence, aiming to improve the reliability of DNA-based data storage. In this paper, we developed a GC-balanced polar code scheme named DNA-BP Code, which stands for balanced polar code for DNA storage, that effectively rectifies IDS errors in DNA storage. The computational complexity of the proposed encoding and decoding algorithms is mathcal{O}(Nlog N) with respect to the code length N. Simulation results show the bit error rate and block error rate as functions of the code length and IDS probability, demonstrating the efficacy of our approach in enhancing the accuracy of DNA storage systems.

In this paper, we propose a low-complexity, secrecy capacity achieving polar coding scheme for the cognitive interference channel with confidential messages (CICC) under the strong secrecy criterion. Existing polar coding schemes for interference channels rely on the use of polar codes for the multiple access channel, the code construction problem of which can be complicated. We show that the whole secrecy capacity region of the CICC can be achieved by simple point-to-point polar codes due to the cognitivity, and our proposed scheme requires the minimum rate of randomness at the encoder.

To reduce the computational complexity of soft-decision (SD) forward error correction (FEC), we propose a polar coding method with a low-complexity successive cancellation decoder. Polar coding induces channel polarization in which two bit-channels with lower and higher reliabilities are polarized. Only the less-reliable bit-channels are protected by SD-FEC, whereas the more-reliable bit-channels are offloaded, reducing the complexity of SD-FEC decoding. The degradation of the bit error ratio (BER) performance can be suppressed by designing the polar encoder structures for the successive cancellation decoder. We numerically demonstrate that the proposed method manages to both reduce the computational complexity by half and suppress the BER performance degradation by less than 0.6 dB, compared with the conventional method using only the SD-FEC.

This paper investigates polar coding schemes achieving capacity for the AWGN channel. The approaches using a multiple access channel with a large number of binary-input users and a single-user channel with a large prime-cardinality input are compared with respect to complexity attributes. The problem of finding discrete approximations to the Gaussian input is then investigated, and it is shown that a quantile quantizer achieves a gap to capacity which decreases like 1/q (where q is the number of constellation points), improving on the 1/log(q) decay achieved with a binomial (central limit theorem) quantizer.

In this paper, we propose partially information coupled bit-interleaved polar coded modulation (PIC-BIPCM), which is a class of spatially coupled polar coding schemes designed for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{Q}$ </tex-math></inline-formula> -ary modulations. Specifically, we consider PIC-BIPCM schemes respectively constructed with three BIPCM schemes: direct BIPCM, punctured BIPCM, and multi-kernel BIPCM. We analyze the error performance of the proposed PIC-BIPCM over the binary erasure channel (BEC) via density evolution. With the analysis as a guideline, we jointly design the positions of coupled bits and the modulation bit-mapper by taking into account the partial polarization of finite length polar codes as well as the unequal error protection of high order modulations. Simulation results demonstrate significant performance improvement of the proposed PIC-BIPCM over the uncoupled BIPCM on both BEC and AWGN channels.