This study will present the design, construction and implementation of Algebraic Geometric Irregular Block Turbo Codes (AGIBTCs). Furthermore, we will evaluate its performance over fast fading channels using different modulation schemes (BPSK, QPSK, 16QAM and 64QAM). The idea behind the design of AGIBTC is to overcome the high system complexity of Algebraic Geometric Block Turbo Codes (AGBTCs) while maintaining a high Bit-Error Rate (BER) performance. This design is inspired by the idea of unequal protection of information symbols which is the core of IBTCs. Our experiments conducted over the worst case of fading channels which is the fast fading channels; and this is done in order to show the magnitude of gain in BER or the reduction in system complexity that can be achieved by this design. Our experiments shows that despite a very slight negative gain over BPSK and QPSK modulation schemes the system complexity is significantly reduced. However, when applying higher modulation schemes a gain in both BER and system complexity are achieved.
In this paper, we investigate in detail the performance of turbo codes in quasi-static fading channels both with and without antenna diversity. First, we develop a simple and accurate analytic technique to evaluate the performance of turbo codes in quasi-static fading channels. The proposed analytic technique relates the frame error rate of a turbo code to the iterative decoder convergence threshold, rather than to the turbo code distance spectrum. Subsequently, we compare the performance of various turbo codes in quasi-static fading channels. We show that, in contrast to the situation in the …
We study irregular binary turbo codes over non-ergodic block-fading channels. We first propose an extension of channel multiplexers initially designed for regular turbo codes. We then show that, using these multiplexers, irregular turbo codes that exhibit a small decoding threshold over the ergodic Gaussian-noise channel perform very close to the outage probability on block-fading channels, from both density evolution and finite-length perspectives.
In this paper, the design of irregular turbo codes for the binary erasure channel is investigated. An analytic expression of the erasure probability of punctured recursive systematic convolutional codes is derived. This exact expression will be used to track the density evolution of turbo codes over the erasure channel, that will allow for the design of capacity-approaching irregular turbo codes. Next, we propose a graph-optimal interleaver for irregular turbo codes. Simulation results for different coding rates is shown at the end.
The purpose of this study is to construct a near capacity Irregular Turbo Code and to evaluate its performance over Gaussian channel. The methodology used to evaluate and measure the performance of the new design is by simulating the system by developing a software platform using Matlab. The simulation carried out by implementing the system over different modulation schemes, different frame sizes, and different code rates in order to achieve a fair comparison between irregular turbo code and regular Turbo Code. The simulation results showed that the Irregular Turbo Code with 64QAM modulation i…
In this work, we discuss techniques for coherently detecting turbo coded orthogonal frequency division multiplexed (OFDM) signals, transmitted through frequency selective Rayleigh (the magnitude of each channel tap is Rayleigh distributed) fading channels having a uniform power delay profile. The channel output is further distorted by a carrier frequency and phase offset, besides additive white Gaussian noise (AWGN). A new frame structure for OFDM, consisting of a known preamble, cyclic prefix, data and known postamble is proposed, which has a higher throughput compared to the earlier work. A …
A telecommunication system uses carriers in order to transmit information through a cable or wirelessly. If each time only one carrier is transmitted, then the system s signal will not be immune to frequency selective fading. If frequency selective fading includes the working frequency of the system, then the wireless link will not be established. Orthogonal frequency division multiplexing OFDM is the primary solution for coping with inter signal interference and frequency selective fading. Many carriers can be produced by splitting a fast information stream to slower data series. Different or…
The minimum average signal-to-noise ratio (SNR) per bit required for error-free transmission over a fading channel is derived, and is shown to be equal to that of the additive white Gaussian noise (AWGN) channel, which is $-1.6$ dB. Discrete-time algorithms are presented for timing and carrier synchronization, as well as channel estimation, for turbo coded multiple input multiple output (MIMO) orthogonal frequency division multiplexed (OFDM) systems. Simulation results show that it is possible to achieve a bit error rate of $10^{-5}$ at an average SNR per bit of 5.5 dB, using two transmit and …
It is known that the frame error rate of turbo codes on quasi-static fading channels can be accurately approximated using the convergence threshold of the corresponding iterative decoder. This paper considers quasi-static fading channels and demonstrates that non-iterative schemes can also be characterized by a similar threshold based on which their frame error rate can be readily estimated. In particular, we show that this threshold is a function of the probability of successful frame detection in additive white Gaussian noise, normalized by the squared instantaneous signal-to-noise ratio. We…
Random access protocols relying on the transmission of packet replicas in multiple slots and exploiting interference cancellation at the receiver have been shown to achieve per- formance competitive with that of orthogonal schemes. So far the optimization of the repetition degree profile, defining the probability for a user to transmit a given number of replicas, has mainly been performed targeting the collision channel model. In this paper the analysis is extended to a block fading channel model, also assuming capture effect at the receiver. Density evolution equations are developed for the n…
As wireless communication systems look intently to compose the transition from voice communication to interactive Internet data, achieving higher bit rates becomes both increasingly desirable and challenging. Space-time coding (STC) is a communications technique for wireless systems that inhabit multiple transmit antennas and single or multiple receive antennas. Space-time codes make use of advantage of both the spatial diversity provided by multiple antennas and the temporal diversity available with time-varying fading. Space-time codes can be divided into block codes and trellis codes. Space…
We solve the problem of designing powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Unfortunately, optimal constructions for maximum-likelihood decoding do not perform well under iterative decoding. To overcome this limitation, we then introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes with multiplexed parallel turbo…
A critical aspect of reliable communication involves the design of codes that allow transmissions to be robustly and computationally efficiently decoded under noisy conditions. Advances in the design of reliable codes have been driven by coding theory and have been sporadic. Recently, it is shown that channel codes that are comparable to modern codes can be learned solely via deep learning. In particular, Turbo Autoencoder (TURBOAE), introduced by Jiang et al., is shown to achieve the reliability of Turbo codes for Additive White Gaussian Noise channels. In this paper, we focus on applying the…
Quadratic permutation polynomials (QPPs) have been widely studied and used as interleavers in turbo codes. However, less attention has been given to cubic permutation polynomials (CPPs). This paper proves a theorem which states sufficient and necessary conditions for a cubic permutation polynomial to be a null permutation polynomial. The result is used to reduce the search complexity of CPP interleavers for short lengths (multiples of 8, between 40 and 352), by improving the distance spectrum over the set of polynomials with the largest spreading factor. The comparison with QPP interleavers is…
In this paper, iterative differential phase-shift keying (DPSK) demodulation and channel decoding scheme is investigated for the Joint Channel decoding and physical layer Network Coding (JCNC) approach in two-way relaying systems. The Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm for both coherent and noncoherent detection is derived for soft-in soft-out decoding of DPSK signalling over the two-user multiple-access channel with Rayleigh fading. Then, we propose a pragmatic approach with the JCNC scheme for iteratively exploiting the extrinsic information of the outer code. With coherent det…
The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading MIMO channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upperbound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders,…
The polar codes are proven to be capacity-achieving and are shown to have equivalent or even better finite-length performance than the turbo/LDPC codes under some improved decoding algorithms over the additive white Gaussian noise (AWGN) channels. Polar coding is based on the so-called channel polarization phenomenon induced by a transform over the underlying binary-input channel. The channel polarization is found to be universal in many signal processing problems and has been applied to the coded modulation schemes. In this paper, the channel polarization is further extended to the multiple a…
Irregular repeat-accumulate Root-Check LDPC codes based on Progressive Edge Growth (PEG) techniques for block-fading channels are proposed. The proposed Root-Check LDPC codes are {both suitable for channels under $F = 2, 3$ independent fadings per codeword and} for fast fading channels. An IRA(A) Root-Check structure is devised for $F = 2, 3$ independent fadings. The performance of the new codes is investigated in terms of the Frame Error Rate (FER). Numerical results show that the IRAA LDPC codes constructed by the proposed algorithm {outperform by about 1dB the existing} IRA Root-Check LDPC …
We consider the problem of recovering channel code parameters over a candidate set by merely analyzing the received encoded signals. We propose a deep learning-based solution that I) is capable of identifying the channel code parameters for any coding scheme (such as LDPC, Convolutional, Turbo, and Polar codes), II) is robust against channel impairments like multi-path fading, III) does not require any previous knowledge or estimation of channel state or signal-to-noise ratio (SNR), and IV) outperforms related works in terms of probability of detecting the correct code parameters.
University of Electronic Science and Technology of China（电子科技大学）；University of California at Davis（加州大学戴维斯分校）
To achieve communication-efficient federated multitask learning (FMTL), we propose an over-the-air FMTL (OAFMTL) framework, where multiple learning tasks deployed on edge devices share a non-orthogonal fading channel under the coordination of an edge server (ES). In OA-FMTL, the local updates of edge devices are sparsified, compressed, and then sent over the uplink channel in a superimposed fashion. The ES employs over-the-air computation in the presence of intertask interference. More specifically, the model aggregations of all the tasks are reconstructed from the channel observations concurr…
In this work, we propose structured Root-Low-Density Parity-Check (LDPC) codes and design techniques for block-fading channels. In particular, Quasi-Cyclic Root-LDPC codes, Irregular repeat-accumulate Root-LDPC codes and Controlled Doping Root-LDPC codes based on Progressive Edge Growth (PEG) techniques for block-fading channels are proposed. The proposed Root-LDPC codes are both suitable for channels under $F = 2, 3$ and $4$ independent fading per codeword. The performance of the proposed codes is investigated in terms of Frame Error Rate (FER). The proposed Root-LDPC codes are capable of ach…
This paper proposes a new method for optimizing frequency-hopping ad hoc networks in the presence of Rayleigh fading. It is assumed that the system uses a capacity-approaching code (e.g., turbo or LDPC) and noncoherent binary continuous-phase frequency-shift keying (CPFSK) modulation. By using transmission capacity as the performance metric, the number of hopping channels, CPFSK modulation index, and code rate are jointly optimized. Mobiles in the network are assumed to be uniformly located within a finite area. Closed-form expressions for outage probability are given for a network characteriz…
In this paper, we design and compare multilevel polar coding (MLPC) and bit-interleaved polar coded modulation (BIPCM) for uplink sparse code multiple access (SCMA) systems that operate over fast and block fading channels. Both successive cancellation (SC) and successive cancellation list (SCL) decoding algorithms are considered. Simulation results show that, with either decoder, BIPCM performs better than its MLPC counterpart. Also, both BIPCM and MLPC exhibit a performance advantage over LTE turbo-coded and WiMAX LDPC SCMA systems when the SCL technique is used for decoding.
In this paper, we propose a novel linear physicallayer network coding (LPNC) for Rayleigh fading 2-way relay channels (2-WRC). Rather than the simple modulo-2 (bit-XOR) operation, the relay directly maps the superimposed signal of the two users into the linear network coded combination in GF(2^2) by multiplying the user data by properly selected generator matrix. We derive the constellation constrained capacities for LPNC and 5QAM denoise-and forward (5QAM-DNF) [2] and further explicitly characterize the capacity difference between LPNC and 5QAM-DNF. Based on our analysis and simulation, we hi…
In this article we focus on the problem of channel decoding in presence of a-priori information. In particular, assuming that the a-priori information reliability is not perfectly estimated at the receiver, we derive a novel analytical framework for evaluating the decoder's performance. It is derived the important result that a "good code", i.e., a code which allows to fully exploit the potential benefit of a-priori information, must associate information sequences with high Hamming weights to codewords with low Hamming weights. Basing on the proposed analysis, we analyze the performance of co…
In this work, we consider transmissions over block fading channels and assume that adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) are implemented. Knowing that in high signal-to-noise ratio, the conventional combination of HARQ with AMC is counterproductive from the throughput point of view, we adopt the so-called layer-coded HARQ (L-HARQ). L-HARQ allows consecutive packets to share the channel and preserves a great degree of separation between AMC and HARQ; this makes the encoding and decoding very simple and allows us to use the available/optimized codes. Num…
In this chapter, we show how the use of differential coding and the presence of phase slips in the transmission channel affect the total achievable information rates and capacity of a system. By means of the commonly used QPSK modulation, we show that the use of differential coding does not decrease the total amount of reliably conveyable information over the channel. It is a common misconception that the use of differential coding introduces an unavoidable differential loss. This perceived differential loss is rather a consequence of simplified differential detection and decoding at the recei…
We consider large MIMO systems, where by `{\em large}' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just $O(N_tN_r)$, where $N_t$ and $N_r$ denote the number of transmit and receive antennas, respe…
This paper proposes a practical successive decoding scheme with finite levels for the finite-state Markov channels where there is no a priori state information at the transmitter or the receiver. The design employs either a random interleaver or a deterministic interleaver with an irregular pattern and an optional iterative estimation and decoding procedure within each level. The interleaver design criteria may be the achievable rate or the extrinsic information transfer (EXIT) chart, depending on the receiver type. For random interleavers, the optimization problem is solved efficiently using …
In this paper, we describe direct-sequence code-division multiple-access (DS-CDMA) systems with quadriphase-shift keying in which channel estimation, coherent demodulation, and decoding are iteratively performed without the use of any training or pilot symbols. An expectation-maximization channel-estimation algorithm for the fading amplitude, phase, and the interference power spectral density (PSD) due to the combined interference and thermal noise is proposed for DS-CDMA systems with irregular repeat-accumulate codes. After initial estimates of the fading amplitude, phase, and interference PS…
In this work, we propose a coding strategy designed to enhance the throughput of hybrid ARQ (HARQ) transmissions over i.i.d. block-fading channels with the channel state information (CSI) unknown at the transmitter. We use a joint packet coding where the same channel block is logically shared among many packets. To reduce the complexity, we use a two-layer coding where, first, packets are first coded by the binary compressing encoders, and the results are then passed to the conventional channel encoder. We show how to optimize the compression rates on the basis of the empirical error-rate curv…
We study an incremental redundancy (IR) cooperative coding scheme for wireless networks. To exploit the spatial diversity benefit we propose a cluster-based collaborating strategy for a quasi-static Rayleigh fading channel model and based on a network geometric distance profile. Our scheme enhances the network performance by embedding an IR cooperative coding scheme into an existing noncooperative route. More precisely, for each hop, we form a collaborating cluster of M-1 nodes between the (hop) sender and the (hop) destination. The transmitted message is encoded using a mother code and partit…
A practical rate-matching system for constructing rate-compatible polar codes is proposed. The proposed polar code circular buffer rate-matching is suitable for transmissions on communication channels that support hybrid automatic repeat request (HARQ) communications, as well as for flexible resource-element rate-matching on single transmission channels. Our proposed circular buffer rate matching scheme also incorporates a bit-mapping scheme for transmission on bit-interleaved coded modulation (BICM) channels using higher order modulations. An interleaver is derived from a puncturing order obt…
Non-orthogonal multiple access (NOMA) is one of the key techniques to address the high spectral efficiency and massive connectivity requirements for the fifth generation (5G) wireless system. To efficiently realize NOMA, we propose a joint design framework combining the polar coding and the NOMA transmission, which deeply mines the generalized polarization effect among the users. In this polar coded NOMA (PC-NOMA) framework, the original NOMA channel is decomposed into multiple bit polarized channels by using a three-stage channel transform, that is, user$\to$signal$\to$bit partitions. Specifi…
This work considers optimizing LDPC codes in the physical-layer network coded two-way relay channel using noncoherent FSK modulation. The error-rate performance of channel decoding at the relay node during the multiple-access phase was improved through EXIT-based optimization of Tanner graph variable node degree distributions. Codes drawn from the DVB-S2 and WiMAX standards were used as a basis for design and performance comparison. The computational complexity characteristics of the standard codes were preserved in the optimized codes by maintaining the extended irregular repeat-accumulate (e…
Low-density parity-check (LDPC) codes are capable of achieving excellent performance and provide a useful alternative for high performance applications. However, at medium to high signal-to-noise ratios (SNR), an observable error floor arises from the loss of independence of messages passed under iterative graph-based decoding. In this paper, the error floor performance of short block length codes is improved by use of a novel candidate selection metric in code graph construction. The proposed Multipath EMD approach avoids harmful structures in the graph by evaluating certain properties of the…
In this paper, the issue of designing an iterative-detection-and-decoding (IDD)-aided receiver, relying on the low-complexity probabilistic data association (PDA) method, is addressed for turbo-coded multiple-input-multiple-output (MIMO) systems using general M-ary modulations. We demonstrate that the classic candidate-search-aided bit-based extrinsic log-likelihood ratio (LLR) calculation method is not applicable to the family of PDA-based detectors. Additionally, we reveal that, in contrast to the interpretation in the existing literature, the output symbol probabilities of existing PDA algo…
