An efficient algorithm for the construction of polar codes for higher-order modulation is presented based on information-theoretic principles. The bit reliabilities after successive demapping are estimated using the LM-rate, an achievable rate for mismatched decoding. The successive demapper bit channels are then replaced by binary input Additive White Gaussian Noise (biAWGN) surrogate channels and polar codes are constructed using the Gaussian approximation (GA). This LM-rate Demapper GA (LM-DGA) construction is used to construct polar codes for several demapping strategies proposed in literature. For all considered demappers, the LM-DGA constructed polar codes have the same performance as polar codes constructed by Monte Carlo (MC) simulation. The proposed LM-DGA construction is much faster than the MC construction. For 64-QAM, spectral efficiency 3 bits/s/Hz, and block length 1536 bits, simulation results show that LM-DGA constructed polar codes with cyclic redundancy check and successive cancellation list decoding are 1 dB more power efficient than state-of-the-art AR4JA low-density parity-check codes.
We consider the problem of using polar codes with higher order modulation over AWGN channels. Unlike prior work, we focus on using modulation independent polar codes. That is, the polar codes are not re-designed based on the modulation used. Instead, we propose bit-permuted coded modulation (BPCM): a technique for using the multilevel coding (MLC) approach for an arbitrary polar code. The BPCM technique exploits a natural connection between MLC and polar codes. It involves applying bit permutations prior to mapping the polar code to a higher order modulation. The bit permutations are designed,…
$2^m$-ary modulation creates $m$ bit channels which are neither independent nor identical, and this causes problems when applying polar coding because polar codes are designed for independent identical channels. Different from the existing multi-level coding (MLC) and bit-interleaved coded modulation (BICM) schemes, this paper provides a convolutional polar coded modulation (CPCM) method that preserves the low-complexity nature of BICM while offering improved spectral efficiency. Numerical results are given to show the good performance of the proposed method.
This paper proposes a new coded modulation scheme for reliable transmission of short data packets at very low signal-to-noise ratio, combining cyclic code shift keying modulation and non-binary polar coding. We consider non-binary polar codes defined over Galois fields, and propose a new design methodology, aimed at optimizing the choice of the kernel coefficients. Numerical results show that the system performance is close to the achievable limits in the finite blocklength regime.
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…
A multilevel coded modulation scheme is studied that uses solely binary polar codes and Honda-Yamamoto probabilistic shaping. The scheme is shown to achieve the capacity of discrete memoryless channels with input alphabets of cardinality a power of two. The performance of finite-length implementations is compared to polar-coded probabilistic amplitude shaping and constant composition distribution matching.
A commonly assumed drawback of multi-level coding, compared to a bit-interleaved coded modulation, is its high latency: Indeed, the levels must be decoded sequentially. In this paper, we consider polar codes to code each level. We show that the decoding time complexity of the multi-level scheme, using successive-cancellation list decoding for each polar code, is only 1.5 times the one of a single polar code, regardless of the signal-to-noise ratio and the number of levels.
Bit-interleaved coded modulation (BICM) and multilevel coded modulation (MLC) are commonly used to combine polar codes with high order modulation. While BICM benefits from simple design and the separation of coding and modulation, MLC shows better performance under successive-cancellation decoding. In this paper we propose a hybrid polar coded modulation scheme that lies between BICM and MLC, wherein a fraction of bits are assigned to set-partition (SP) labeling and the remaining bits are assigned for Gray labeling. The SP labeled bits undergo sequential demodulation, using iterative demodulat…
In this letter, we propose a progressive rate-filling method as a framework to study agile construction of multilevel polar-coded modulation. We show that the bit indices within each component polar code can follow a fixed, precomputed ranking sequence, e.g., the Polar sequence in the 5G standard, while their allocated rates (i.e., the number of information bits of each component polar code) can be fast computed by exploiting the target sum-rate approximation and proper rate-filling methods. In particular, we develop two rate-filling strategies based on the capacity and the rate considering th…
Non-orthogonal multiple access (NOMA) schemes have been proved to increase the multiple-access achievable rate with respect to orthogonal multiple access (OMA). In this paper we propose a novel communication system that combines multi-level coded modulation and polar codes in a NOMA scenario. Computational complexity decreases with the proposed scheme with respect to state-of-the-art solutions. We also highlight the trade-off between error rate performance and computational complexity.
BMERA or convolutional polar codes are an extension of polar codes with a provably better error exponent than polar codes. A successive cancellation (SC) decoding algorithm for BMERA codes similar to SC polar decoders is introduced. A pseudocode description of the SC decoder that can be extended to SC list (SCL) decoding is provided. Simulation results with and without outer CRC codes under SC and SCL decoding are presented for QAM modulation over the AWGN channel to compare the performance of polar and BMERA codes. BMERA codes outperform polar codes by more than 0.5 dB under SCL decoding with…
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.
We consider probabilistic shaping to maximize the achievable information rate of coded modulation (CM) with hard decision decoding. The proposed scheme using binary staircase codes outperforms its uniform CM counterpart by more than 1.3 dB for 64-QAM and 5 bits/symbol.
In this paper, we represent Raptor codes as multi-edge type low-density parity-check (MET-LDPC) codes, which gives a general framework to design them for higher-order modulation using MET density evolution. We then propose an efficient Raptor code design method for higher-order modulation, where we design distinct degree distributions for distinct bit levels. We consider a joint decoding scheme based on belief propagation for Raptor codes and also derive an exact expression for the stability condition. In several examples, we demonstrate that the higher-order modulated Raptor codes designed us…
In this paper we present a novel modulation technique for dual polarization communication systems, which reduces the error rate compared with the existent schemes. This modulation places the symbols in a 3D constellation, rather than the classic approach of 2D. Adjusting the phase of these symbols depending on the information bits, we are able to increase the bit rate. Hence, the proposed scheme conveys information by selecting both polarization state and the phase of radiated electromagnetic wave. We also analyse the performance of 3D Polarized Modulation (PMod) for different constellation si…
In this paper, density evolution-based construction methods to design good polar codes on impulsive noise channels for single-carrier and multi-carrier systems are proposed and evaluated. For a single-carrier system, the tight bound of the block error probability (BLEP) is derived by applying density evolution and the performance of the proposed construction methods are compared. For the multi-carrier system employing orthogonal frequency-division multiplexing, the accurate BLEP estimation is not feasible so a tight lower bound on the BLEP for polar codes is derived by assuming the noise on ea…
Typically, forward error correction (FEC) codes are designed based on the minimization of the error rate for a given code rate. However, for applications that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive modulation and coding, the throughput is a more important performance metric than the error rate. Polar codes, a new class of FEC codes with simple rate matching, can be optimized efficiently for maximization of the throughput. In this paper, we aim to design HARQ schemes using multilevel polar coded-modulation (MLPCM). Thus, we first develop a method to determine a…
The capacity of the AWGN broadcast channel is achieved by superposition coding, but superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Coded modulation over a broadcast channel subject to a specific channel-input modulation constraint remains an important open problem. Some progress has been made in the related area of unequal-error protection modulations which can be considered single-user broadcast transmission, but it does not approach all points on the boundary of the capacity region. This paper studies broadcast coded modulation u…
In this paper, we propose a novel joint coding-modulation technique based on serial concatenation of orthogonal linear transform, such as discrete Fourier transform (DFT) or Walsh-Hadamard transform (WHT), with memoryless nonlinearity. We demonstrate that such a simple signal construction may exhibit properties of a random code ensemble, as a result approaching channel capacity. Our computer simulations confirm that if the decoder relies on a modified approximate message passing algorithm, the proposed modulation technique exhibits performance on par with state-of-the-art coded modulation sche…
In this paper, we propose a new class of nonbinary polar codes with two-stage polarization for ultra-reliable and low-latency communications (URLLC), where the outer (symbol-level) polarization is achieved by using a 2X2 q-ary matrix [1 0; β1] as the kernel and the inner (bit-level) polarization is achieved by a binary polarization matrix for each input symbol. With the two-stage polarization, bit-level code construction is introduced, resulting in partially-frozen symbols, where the frozen bits in these symbols can be used as active-check bits to facilitate the decoder. The encoder/decoder of…
This paper introduces a novel class of code sets, called "symmetrical Z-complementary code sets (SZCCSs)" , whose aperiodic auto- and cross- correlation sums exhibit zero-correlation zones (ZCZs) at both the front-end and tail-end of the entire correlation window. Three constructions of (optimal) SZCCSs based on general Boolean functions are presented. As a second major contribution, we apply SZCCSs to design optimal training sequences for broadband generalized spatial modulation (GSM) systems over frequency-selective channels. Key words: Complementary code set, channel estimation, training se…
Spatial complementary code keying modulation (SCCKM) is proposed as a novel block coding modulation scheme. An input binary sequence is modulated based on the different lengths of complementary code keying (CCK) modulation and then spread across the transmit antennas (spatial domain) in a multiple input multiple output (MIMO) system exploiting orthogonal frequency division multiplexing (OFDM). At the receiver side, zero forcing equalization is applied to the OFDM modulated data to mitigate the effect of the multipath fast fading channel and then followed by maximum likelihood (ML) detection to…
Generalized product codes (GPCs) are extensions of product codes (PCs) where coded bits are protected by two component codes but not necessarily arranged in a rectangular array. It has recently been shown that there exists a large class of deterministic GPCs (including, e.g., irregular PCs, half-product codes, staircase codes, and certain braided codes) for which the asymptotic performance under iterative bounded-distance decoding over the binary erasure channel (BEC) can be rigorously characterized in terms of a density evolution analysis. In this paper, the analysis is extended to the case w…
We propose a hybrid coded modulation scheme which composes of inner and outer codes. The outer-code can be any standard binary linear code with efficient soft decoding capability (e.g. low-density parity-check (LDPC) codes). The inner code is designed using a deep neural network (DNN) which takes the channel coded bits and outputs modulated symbols. For training the DNN, we propose to use a loss function that is inspired by the generalized mutual information. The resulting constellations are shown to outperform the conventional quadrature amplitude modulation (QAM) based coding scheme for modu…
This paper investigates the design of spatially coupled low-density parity-check (SC-LDPC) codes constructed from connected-chain ensembles for bit-interleaved coded modulation (BICM) schemes. For short coupling lengths, connecting multiple SC-LDPC chains can improve decoding performance over single-chains and impose structured unequal error protection (UEP). A joint design of connected-chain ensembles and bit mapping to further exploit the UEP from codes and high-order modulations is proposed. Numerical results demonstrate the superiority of the proposed design over existing connected-chain e…
In this paper, we propose two novel modulation concepts based on a simple maximum distance separable (MDS) code { and show that these concepts can achieve better error performance than index modulation (IM) and related schemes.} In the first concept, we use amplitude and phase levels to form a simple MDS code, whereas, in the second one, in-phase and quadrature components of codeword elements are used to construct the MDS code. We depict practical schemes for using the proposed concepts with orthogonal frequency division multiplexing (OFDM). We analyze the performance in terms of the minimum E…
Delayed bit-interleaved coded modulation (DBICM) generalizes bit-interleaved coded modulation (BICM) by modulating differently delayed sub-blocks of codewords onto the same signals. DBICM improves transmission reliability over BICM due to its capability of detecting undelayed sub-blocks with the extrinsic information of the decoded delayed sub-blocks. In this work, we propose a novel windowed decoding algorithm for DBICM, which uses the extrinsic information of both the decoded delayed and undelayed sub-blocks, to improve the detection on all sub-blocks. Numerical results show that the propose…
We study permutations over the set of $\ell$-grams, that are feasible in the sense that there is a sequence whose $\ell$-gram frequency has the same ranking as the permutation. Codes, which are sets of feasible permutations, protect information stored in DNA molecules using the rank-modulation scheme, and read using the shotgun sequencing technique. We construct systematic codes with an efficient encoding algorithm, and show that they are optimal in size. The length of the DNA sequences that correspond to the codewords is shown to be polynomial in the code parameters. Non-systematic with large…
Graduate Institute of Electrical Engineering, National Taiwan University（台湾大学电机工程学研究所）
To develop intelligent receivers, automatic modulation classification (AMC) plays an important role for better spectrum utilization. The emerging deep learning (DL) technique has received much attention in AMC due to its superior performance in classifying data with deep structure. In this work, a novel polar-based deep learning architecture with channel compensation network (CCN) is proposed. Our test results show that learning features from polar domain (r-theta) can improve recognition accuracy by 5% and reduce training overhead by 48%. Besides, the proposed CCN is also robust to channel fa…
