We consider the problem of supporting H-ARQ with polar codes. For supporting H-ARQ, we propose to create redundancy versions based on different, but equivalent, subsets of a polar code. The equivalent subsets are created from an initial subset of a polar code using an inherent symmetry in polar code construction. A greedy construction is used to create the initial subset of a polar code. We demonstrate performance of proposed constructions via simulations for binary input AWGN channel. We demonstrate that a (4096, 1024) polar code can be divided into two disjoint (2048, 1024) subset polar codes, which when decoded individually are within 0.2 dB (at $1 \%$ BLER) of a (2048, 1024) polar code, and achieve performance of a (4096, 1024) polar code when decoded jointly.
We analyze the performance of amplify-and-forward (AF) automatic repeat request (ARQ) for a two-hop cooperative system with reliability constrains. For this setup, we first derive the closed-form outage probability expression. Next, we present a power allocation scheme that allows us to achieve a target outage probability, while minimizing the outage-weighted average power expenditure for asymmetric power allocation between the source and relay. This is cast as an optimization problem, and the optimal power allocation (OPA) is obtained in closed form by invoking the Karush-Kuhn-Tucker (KKT) co…
We propose two schemes for selective-repeat ARQ protocols over packet erasure channels with unreliable feedback: (i) a hybrid ARQ protocol with soft combining at the receiver, and (ii) a coded ARQ protocol, by building on the uncoded baseline scheme for ARQ, developed by Ausavapattanakun and Nosratinia. Our method leverages discrete-time queuing and coding theory to analyze the performance of the proposed data transmission methods. We incorporate forward error-correction to reduce in-order delivery delay, and exploit a matrix signal-flow graph approach to analyze the throughput and delay of th…
This paper presents a novel opportunistic spectrum sharing scheme that applies ARQ protocol to achieve ultra reliability in the finite blocklength regime. A primary user shares its licensed spectrum to a secondary user, where both communicate to the same base station. The base station applies ARQ with the secondary user, which possess a limited number of trials to transmit each packet. We resort to the interweave model in which the secondary user senses the primary user activity and accesses the channel with access probabilities which depend on the primary user arrival rate and the number of a…
Future 5G systems will need to support ultra-reliable low-latency communications scenarios. From a latency-reliability viewpoint, it is inefficient to rely on average utility-based system design. Therefore, we introduce the notion of guaranteeable delay which is the average delay plus three standard deviations of the mean. We investigate the trade-off between guaranteeable delay and throughput for point-to-point wireless erasure links with unreliable and delayed feedback, by bringing together signal flow techniques to the area of coding. We use tiny codes, i.e. sliding window by coding with ju…
A hybrid ARQ (HARQ) scheme for polar code, which is called active-bit relocation under masks (ARUM), is proposed. In each transmission, the data bits are encoded and bit-wisely XOR-masked using a binary vector before being transmitted through the channel. The masking process combines multiple transmissions together which forms another step of inter-transmission channel transform. The reliabilities are updated after every transmission, and the less reliable bits in earlier ones are relocated to the more reliable positions at the latest transmitted block. ARUM is a very flexible HARQ scheme whic…
The rateless and information additive properties of fountain codes make them attractive for use in broadcast/multicast applications, especially in radio environments where channel characteristics vary with time and bandwidth is expensive. Conventional schemes using a combination of ARQ (Automatic Repeat reQuest) and FEC (Forward Error Correction) suffer from serious drawbacks such as feedback implosion at the transmitter, the need to know the channel characteristics apriori so that the FEC scheme is designed to be effective and the fact that a reverse channel is needed to request retransmissio…
We propose a unitary precoding scheme, namely polar-precoding, to improve the performance of polar-coded MIMO systems. In contrast to the traditional design of MIMO precoding criteria, the proposed polar-precoding scheme relies on the \emph{polarization criterion}. In particular, the precoding matrix design comprises two steps. After selecting a basic matrix for maximizing the capacity in the first step, we design a unitary matrix for maximizing the polarization effect among the data streams without degrading the capacity. Our simulation results show that the proposed polar-precoding scheme ou…
The long-haul communication systems can offer ultra high-speed data transfer rates but suffer from burst errors. The high-rate and high-performance staircase codes provide an efficient way for long-haul transmission. The staircase coding scheme is a concatenation structure, which provides the opportunity to improve the performance of high-rate polar codes. At the same time, the polar codes make the staircase structure more reliable. Thus, a high-rate polar-staircase coding scheme is proposed, where the systematic polar codes are applied as the component codes. The soft cancellation decoding of…
A flexible incremental redundancy hybrid auto- mated repeat request (IR-HARQ) scheme for polar codes is proposed based on dynamically frozen bits and the quasi-uniform puncturing (QUP) algorithm. The length of each transmission is not restricted to a power of two. It is applicable for the binary input additive white Gaussian noise (biAWGN) channel as well as higher-order modulation. Simulation results show that this scheme has similar performance as directly designed polar codes with QUP and outperforms LTE-turbo and 5G-LDPC codes with IR-HARQ.
Two concatenated coding schemes incorporating algebraic Reed-Solomon (RS) codes and polarization-adjusted convolutional (PAC) codes are proposed. Simulation results show that at a bit error rate of $10^{-5}$, a concatenated scheme using RS and PAC codes has more than $0.25$ dB coding gain over the NASA standard concatenation scheme, which uses RS and convolutional codes.
A new polar coding scheme for higher order modulation is presented. The proposed scheme is based on multi-level coding (MLC) with natural labeling, where the bit-level corresponding to the sign-bit is generated in dependence on the previous bit-levels, such that the modulated symbols are distributed according to a target non-uniform distribution resulting in a shaping gain. This is realized by replacing the polar encoder in the sign-bit level by a successive cancellation (SC) decoder, such that the overall complexity is not increased compared to a conventional MLC scheme with polar codes. Nume…
It is known that the bit errors of polar codes with successive cancellation (SC) decoding are coupled. However, existing concatenation schemes of polar codes with other error correction codes rarely take this coupling effect into consideration. To achieve a better error performance of concatenated systems with polar codes as inner codes, one can divide all bits in an outer block into different polar blocks to completely de-correlate the possible coupled errors in the transmitter side. We call this interleaving a blind interleaving (BI) which serves as a benchmark. Two BI schemes, termed BI-DP …
This paper presents a coding scheme for an insertion deletion substitution channel. We extend a previous scheme for the deletion channel where polar codes are modified by adding "guard bands" between segments. In the new scheme, each guard band is comprised of a middle segment of '1' symbols, and left and right segments of '0' symbols. Our coding scheme allows for a regular hidden-Markov input distribution, and achieves the information rate between the input and corresponding output of such a distribution. Thus, we prove that our scheme can be used to efficiently achieve the capacity of the ch…
A polar-coded modulation scheme for deep-space optical communication is proposed. The photon counting Poisson channel with pulse position modulation (PPM) is considered. We use the fact that PPM is particularly well suited to be used with multilevel codes to design a polar-coded modulation scheme for the system in consideration. The construction of polar codes for the Poisson channel based on Gaussian approximation is demonstrated to be accurate. The proposed scheme uses a cyclic redundancy check outer code and a successive cancellation decoder with list decoding and it is shown that it outper…
In this paper, we propose a new polar coding scheme for the unsourced, uncoordinated Gaussian random access channel. Our scheme is based on sparse spreading, treat interference as noise and successive interference cancellation (SIC). On the transmitters side, each user randomly picks a code-length and a transmit power from multiple choices according to some probability distribution to encode its message, and an interleaver to spread its encoded codeword bits across the entire transmission block. The encoding configuration of each user is transmitted by compressive sensing, similar to some prev…
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 c…
Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5th generation (5G) wireless standard. Most polar code research examines the original Arikan polar coding scheme, which is limited in block length to powers of two. This constraint presents a considerable obstacle since practical applications call for all code lengths to be readily available. Puncturing and shortening techniques allow for flexible polar codes, while multi-kernel polar codes produce native code lengths that are powers of two and/or three.…
We consider a problem of unsourced random access in the quasi-static Rayleigh fading channel. In the previous work, the authors have proposed LDPC code based solutions based on joint and treat interference as noise in combination with successive interference cancellation (TIN-SIC) decoder architectures. The authors showed that TIN-SIC decoding significantly outperforms the joint decoding approach and much simpler from the implementation point of view. In this paper, we continue the analysis of TIN-SIC decoding. We derive a finite length achievability bound for TIN-SIC decoder using random codi…
The adversarial wiretap channel (AWTC) model is a secure communication model in which adversary can directly read and write the transmitted bits in legitimate communication with fixed fractions. In this paper we propose a secure polar coding scheme to provide secure and reliable communication over the AWTC model. For the adversarial reading and writing action, we present a $ρ$ equivalent channel block and study its transformation under the channel polarization operation. We find that the generated channels are polarized in the sense that part of them are full-noise channels with probability al…
We design polar codes for empirical coordination and strong coordination in two-node networks. Our constructions hinge on the fact that polar codes enable explicit low-complexity schemes for soft covering. We leverage this property to propose explicit and low-complexity coding schemes that achieve the capacity regions of both empirical coordination and strong coordination for sequences of actions taking value in an alphabet of prime cardinality. Our results improve previously known polar coding schemes, which (i) were restricted to uniform distributions and to actions obtained via binary symme…
In this paper, we first propose an universal polar coding scheme for parallel Gaussian channels with non-binary inputs. It is assumed that the encoder knows only the sum capacity of M parallel channels instead of the capacity of any single channel. By decomposing each parallel channel into T = [log2r] sub channels, we therefore obtain MT binary sub-channels. A super polar coding scheme that across all sub-channels is then proposed. This scheme can achieve the sum capacity when the block length is sufficiently large. We have also discussed the applications of parallel polar coding design for bo…
