Polar Coding Strategies for the Interference Channel With Partial-Joint Decoding

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.

The best known inner bound on the two-receiver general broadcast channel without a common message is due to Marton [3]. This result was subsequently generalized in [2, p. 391, Problem 10(c)] and [4] to broadcast channels with a common message. However the latter region is not computable (except in certain special cases) as no bounds on the cardinality of its auxiliary random variables exist. Nor is it even clear that the inner bound is a closed set. The main obstacle in proving cardinality bounds is the fact that the Caratheodory theorem, the main known tool for proving cardinality bounds, does not yield a finite cardinality result. Our new tool is based on an identity that relates the second derivative of the Shannon entropy of a discrete random variable (under a certain perturbation) to the corresponding Fisher information. In order to go beyond the traditional Caratheodory type arguments, we identify certain properties that the auxiliary random variables corresponding to the extreme points of the inner bound satisfy. These properties are then used to establish cardinality bounds on the auxiliary random variables of the inner bound, thereby proving the computability of the region, and its closedness. Although existence of cardinality bounds renders Marton's inner bound computable, it is still hard to evaluate the region. It is however shown that the computation can be significantly simplified if we further assume that Marton's inner bound and the recent outer bound of Nair and El Gamal match at the given particular channel. In order to demonstrate this, we consider a large class of binary input broadcast channels and compute maximum of the sum rate of private messages assuming that the inner and the outer bound match at the given broadcast channel. We also show that the inner and the outer bound do not match for some broadcast channels, thus establishing a conjecture of [15].

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.

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.

A long-standing vision of backscatter communications is to provide long-range connectivity and high-speed transmissions for batteryless Internet-of-Things (IoT). Recent years have seen major innovations in designing backscatters toward this goal. Yet, they either operate at a very short range, or experience extremely low throughput. This paper takes one step further toward breaking this stalemate, by presenting PolarScatter that exploits channel polarization in long-range backscatter links. We transform backscatter channels into nearly noiseless virtual channels through channel polarization, and convey bits with extremely low error probability. Specifically, we propose a new polar code scheme that automatically adapts itself to different channel quality, and design a low-cost encoder to accommodate polar codes on resource-constrained backscatter tags. We build a prototype PCB tag and test it in various outdoor and indoor environments. Our experiments show that our prototype achieves up to 10× throughput gain, or extends the range limit by 1.8× compared with the state-of-the-art long-range backscatter solution. We also simulate an IC design in TSMC 65 nm LP CMOS process. Compared with traditional encoders, our encoder reduces storage overhead by three orders of magnitude, and lowers the power consumption to tens of microwatts.

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.

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.

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.

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.

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.

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.

In this paper, a new rateless scheme of polar codes is designed via extending and puncturing for unknown AWGN channel. In the proposed scheme, a heuristic and pragmatic construction method of polar codes is utilized for rateless coding, which could be applied for time-varying channel. By copying information bits to more reliable bit channels when extending the codes, the scheme could obtain full coding gain. Moreover, to improve throughput performance, we explore the optimal initial coding rate of first transmission to achieve maximal throughput. Simulation results indicate that our proposed rateless scheme could improve block error rate (BLER) and throughput performance in contrast to the existing scheme.

The Schalkwijk-Kailath (SK) scheme for the AWGN channel with noise-free feedback is well-known since its coding complexity grows linearly with the coding blocklength, and it is capacity-achieving and has extremely lower decoding error probability comparing with existing excellent codes such as LDPC and Polar codes. However, extension of SK scheme to more practical scenarios is challenging since it depends heavily on the feedback success. This paper aims to investigate how to design SK-type schemes for channels with intermittent feedback and establish the relationship between the coding blocklength, the desired decoding error probability, the achievable transmission rate and secrecy level of our proposed schemes. Specifically, first, for the additive white Gaussian noise (AWGN) channel with intermittent noise-free feedback, a variation of the well-known Schalkwijk-Kailath (SK) scheme for the AWGN channel with noise-free feedback is proposed, and the corresponding achievable rate is characterized for given coding blocklength and decoding error probability. Subsequently, the proposed scheme is extended to channels with noisy intermittent feedback. To quantitatively evaluate the secrecy performance, we adopt the eavesdropper's normalized equivocation as the secrecy metric and analytically characterize the achievable secrecy level of the proposed schemes. In particular, we show that perfect weak secrecy, i.e., asymptotically vanishing information leakage rate, can be achieved under certain conditions. Numerical results show that for a given decoding error probability threshold, our proposed schemes require lower signal-to-noise ratio and significantly shorter coding blocklength comparing with LDPC code. The study of this paper may provide a way to construct efficient coding scheme for channels in the presence of intermittent feedback.

In this paper, we propose a novel polar code construction scheme, suitable for the underwater acoustic (UWA) multi-user communication system using orthogonal frequency division multiplexing (OFDM). We use the polar codes because the code rate of a polar code can be arbitrarily designed. Moreover, the polar codes can also be used to create a nested code structure, divided into several subsets (codebook). We exploit this feature of the polar codes and place the information bits in the codebook to avoid superimposition of all the users. This helps to eliminate the influence of the power allocation coefficient and make full use of the power of the transducer at the transmitted node. Furthermore, the proposed scheme maximizes the utilization efficiency of the OFDM subcarrier resource for each user by avoiding null pilot tones that are usually required for channel equalization in the traditional schemes. The proposed scheme also does not depend on the channel state information (CSI) as prior information as each user can decode their own data independently by using their own codebook without successive interference cancellation (SIC). The simulation and tank experiment results demonstrate that the proposed scheme can significantly guarantee the reliability of all the users, and reduces the complexity of the receiver, thus making it most suitable for the downlink UWA multi-user communication systems.

It is shown that polar coding schemes achieve the known achievable rate regions for several multi-terminal communications problems including lossy distributed source coding, multiple access channels and multiple descriptions coding. The results are valid for arbitrary alphabet sizes (binary or nonbinary) and arbitrary distributions (symmetric or asymmetric).