Multistage Decoding Research Articles

A Novel Cooperative Communication System Based on Multilevel Convolutional Codes

The authors propose a system where single antenna mobile users share antennas to transmit their information cooperatively to the common base station. Each mobile user overhears the coded information transmitted by other users, detects it and further encodes it along with its own information. The encoding is done using multilevel coding scheme with convolutional codes as component codes. The proposed system considers the self-information of user u at level u to reduce complexity while decoding. The coded symbols are mapped to M-ary quadrature amplitude modulation constellation using multi-resolution modulation partitioning. This enables the component codes to be designed for lower order constellation. Each cooperative user transmits multilevel coded symbols to the common base station, thus creating transmit diversity. The base station receives noisy superposition of independent Rayleigh faded signals transmitted by cooperative users and pass it through a multistage decoder. The multistage decoder employs maximum likelihood based Viterbi decoder at each stage to detect the information of each user. The Viterbi decoder applies max-log approximation to reduce the branch metric complexity. The proposed cooperative multilevel coding system outperforms non-cooperative multilevel coding system and is less complex than the existing cooperative multilevel coding system.

Construction πA and πD Lattices: Construction, Goodness, and Decoding Algorithms

A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of $L$ linear codes over $\mathbb {F}_{p_{1}},\ldots ,\mathbb {F}_{p_{L}}$ , respectively, and hence is referred to as Construction $\pi _{A}$ . The existence of a sequence of such lattices that is good for channel coding (i.e., Poltyrev-limit achieving) under multistage decoding is shown. A new family of multilevel nested lattice codes based on Construction $\pi _{A}$ lattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction $\pi _{D}$ is also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction $\pi _{A}$ as special cases.

Multilevel spatial modulation

In this paper, a new Multilevel Spatial Modulation technique is proposed. It combines computationally efficient multilevel oding and spatial modulation based on trellis codes to increase coding gain, diversity gain, and bandwidth efficiency. The trellis complexity of the single-stage system increases exponentially, whereas in the proposed multilevel system the complexity increases linearly. The proposed system is analyzed with optimal Viterbi and suboptimal sequential decoding algorithms. The results show that sequential decoding saves 75% of the computational power with a loss of 2 dB SNR approximately, when compared with optimal Viterbi decoding, over both fast- and slow-fading channel conditions. Since the antenna index is used as a source of information in spatial modulation, the number of antennae required increases with the throughput and packing a large number of antennas make cross-correlation unavoidable. In this paper, a low complexity modified decoding technique is also proposed for the multilevel spatial modulation system, in which the correlated received signals are equally combined and decoded by the multistage decoder using the Viterbi algorithm. This technique exploits the receiver antenna correlation and makes the decoding complexity independent of number of antennas. The simulation results indicate that the proposed low complexity algorithm gives approximately 8–10 dB gain when compared with optimal Viterbi decoder with equivalent computational complexity when the eight highly correlated signals are equally combined. This may be a suitable solution for mobile handsets where size and computational complexity are the major issues.

Binary polar codes are optimised codes for bitwise multistage decoding

Polar codes are considered the latest major breakthrough in coding theory. Polar codes were introduced by Ar{\i}kan in 2008. In this letter, we show that the binary polar codes are the same as the optimized codes for bitwise multistage decoding (OCBM), which have been discovered before by Stolte in 2002. The equivalence between the techniques used for the constructions and decodings of both codes is established.

Multilevel Coded Modulation With Reduced Latency Decoding Based on Novel Set Partitioning for APSK

We address the use of a multilevel coding (MLC) to the amplitude phase-shift keying (APSK) modulations that consist of multiple PSK rings of different radii with a distinct number of constellation points. Such modulations have been adopted in the satellite broadcasting standards since they have a significant advantage over commonly used square-type quadrature amplitude modulations; their signals exhibit lower peak-to-average power ratio and thus enhance the power amplifier efficiency at the transmitter. A common low-complexity approach for decoding of MLC is the multi-stage decoding (MSD). However, MSD in general leads to severe latency at the decoder since the binary decisions on the higher levels should wait for those of the lower levels. Furthermore, this latency issue is even more salient for APSK signaling due to its circular nature of constellations that does not allow its decomposition into in-phase and quadrature components (i.e., I-Q decomposition). Therefore, in this paper we introduce a new MLC design for APSK that enables the decoder to reduce its latency without any increase in terms of complexity. The proposed approach consists of a novel labeling with an unconventional set partitioning that allows the detector to make use of I-Q decomposition. Specifically, the proposed set partitioning results in a quadrature-PSK constellation at the penultimate level, which can be decomposed into a pair of separately decodable binary-PSK constellations at the final level. The resulting decoder consists of a combination of MSD and parallel independent decoding that can be implemented with lower latency. The simulation results together with the theoretical analyses demonstrate that the reduction of not only the decoding latency but also the complexity in bit metric calculation can be achieved without noticeable degradation in terms of error performance compared to the conventional set partitioning approach.

Efficient LLR estimation for multistage decoding

Multilevel coding (MLC) provides a low-complexity encoding scheme for lattices obtained via construction D. On the other hand, multistage decoding is also a practical decoding scheme for MLC provided that the underlying error correcting codes are capacity achieving, which requires using a powerful soft decoder for each code. In this article, we propose an approximation of the log-likelihood ratio (LLR) used for the soft decoding of the different error correcting codes employed in the lattice construction. This approximation is based on the von Mises distribution and achieves,with lower complexity, the same error rate performance obtained with the exact LLR calculation.

Design of 1, 024 × 16 cm8SRAM Using Self-time and Other Power Reduction Techniques

SRAM design is very crucial as it takes a large fraction of total power and die area in high-performance processors. The performance of embedded memory and its peripheral circuits can adversely affect the speed and power of the overall system. This paper explores the design of SRAM focusing on optimising delay, reducing power and layout area. The key to low power operation of the design is self-timed architecture, multi stage decoding and full custom approach. A 1, 024 × 16 SRAM is designed using Predictive Technology Model BSIM 4 Bulk at 180 nm technology with 1 V power supply (VDD). The aspect ratio that is W/L of the transistors used in an SRAM cell is taken in the range 0.6 < W/L < 1.8. Complete read/write, self-time and other simulations were carried to substantiate the techniques implemented in this paper.

A map-based image steganography scheme for RGB images

Majority of research in steganography focuses on hiding the secret information into the cover directly. The payload can be more secured by not embedding the secret in the cover at all. Instead, a partial information about the secret may be embedded which can be used for later payload realisation. This typically appears analogous to random noise and cannot regenerate the payload without a key. Common approaches to achieve such information include pre-embedding payload encryption. However, simpler cover-secret map-based techniques can also be thought of where such information is generated with optimal resource utilisation. This paper proposes a map-based data hiding scheme in images through image realisation steganography. The proposed technique works for colour and grey images. It also incorporates a multi-stage decoding key and there have been efforts to ensure that the technique conforms to high fidelity of the stego image and performs decently against steganalysis attacks.

Design and Analysis of Multi-Level Physical-Layer Network Coding for Gaussian Two-Way Relay Channels

In this paper, we propose a multi-level physical-layer network coding (MPLNC) scheme that optimizes the relay performance for both symmetric and asymmetric traffic in a Gaussian two-way relay channel. The proposed MPLNC scheme enables each source to employ multiple linear binary codes for encoding, one per modulation level, and the relay node to decode superimposed network codewords at each modulation level. We first derive the achievable rate for the transmission of arbitrary constellations and then prove that MPLNC with multistage decoding (MPLNC/MSD) can achieve the achievable rate if binary code rates are properly chosen for both sources. Furthermore, the design criteria for the proposed MPLNC scheme is investigated, which includes the rate design rule and the labeling strategy. Moreover, we derive the error exponent and an upper bound of the overall error probability for MPLNC. Our analysis and simulation results show that MPLNC/MSD has a significant performance advantage in comparison to the existing bit-interleaved coded modulation (BICM)-based PLNC scheme.

Multi-Level Coded Modulation for 16-ary Constellations in Presence of Phase Noise

Application of multi-level coded modulation (MLCM) for 16-ary constellations in coherent systems is studied. An MLCM system with Reed-Solomon component codes and multi-stage decoder is considered. A systematic numerical method for finding set-partitioning and optimal code rates is presented. The method only requires the probability density function of received samples and can be applied to any constellation regardless of irregularity or lack of symmetry. Performance of the designed MLCM system is verified in presence of nonlinear phase noise and normal phase noise. For nonlinear phase noise limited system, it is shown that the block error rate (BLER) of the system can be improved using our approach for set-partitioning. For phase noise limited system, both BLER and bit error rate (BER) are studied for a phase noise optimized and square 16-quadrature amplitude modulation (16QAM). Post forward-error correction (FEC) BER performance of the optimized constellation over square 16QAM is studied for different levels of phase noise. It is shown that the optimized constellation along with MLCM system decreases the required signal-to-noise ratio by several dB at high phase noise regime and low post FEC BER.

Improving the performance of BICM-ID and MLC systems with different FEC codes

Abstract. In bandwidth limited communication systems, the high data rate transmission with performance close to capacity limits is achieved by applying multilevel modulation schemes in association with powerful forward error correction (FEC) coding, i.e. coded modulation systems. The most important practical approaches to coded modulation systems are multilevel coding with multistage decoding (MLC/MSD) and bit interleaved coded modulation with iterative demapping and decoding (BICM-ID). Multilevel modulation formats such as M-QAM, which can be used as a part of coded modulation systems, have the capability of multilevel protection. Based on this fact, we investigate the methods to improve the performance of BICM-ID using multiple interleavers with different binary channel coding schemes such as convolutional codes, turbo codes and low-density parity-check (LDPC) codes. Moreover, an MLC system with parallel decoding on levels (PDL) at the receiver is considered. In our contribution, we propose to design the individual coding schemes using the extrinsic information transfer (EXIT) charts for individual bit levels in the constellation. Our simulation results show that the BICM-ID systems, taking into account different bit-level protections, can provide an improvement of 0.65 dB, 1.2 dB and 1.5 dB for 256-QAM with turbo, LDPC and convolutional codes, respectively. On the other hand, MLC systems with PDL designed using EXIT charts for individual bit levels can slightly improve the performance and eliminate the error floor compared to the systems with MSD.

Improved Hard Iterative Decoding (IHID) of Multilevel Codes

An improved hard iterative decoding (IHID) algorithm is presented to efficiently terminate hard iterations in the decoding of multi-level codes. The proposed terminating policy stops iterations as soon as a valid path on the super trellis is found thereby only running the minimum required number of iterations. The IHID decoding algorithm performs better than the conventional multi-stage decoding by reducing the effects of error multiplicity. Compared with known hard iterative decoding with fixed number of iterations, the IHID algorithm can significantly reduce decoding complexity and decoding delay.

RS-Enhanced TCM for Multilevel Flash Memories

Multilevel flash memories store more than one bit per storage cell and are further characterized by large word (page) sizes and very low target error rates. In this paper, a high-rate error control scheme is presented that uses inner trellis-coded modulation (TCM) for storing two bits per cell with five possible charge levels. The coded subset-label bits and the uncoded signal-label bits of TCM are independently protected by separate outer Reed-Solomon (RS) codes. The resulting scheme permits multistage decoding. Errors made by the TCM decoder in the subset-label bits occur in bursts and are corrected by the associated first RS decoder prior to determining signal-label bits and correcting errors in those bits by the associated second RS decoder. The multi-stage decoding avoids the significant spread of errors from subset-label bits into the generally larger number of signal-label bits which is typical for conventional serial RS-TCM concatenation when the inner TCM system operates at relatively low SNR. The error performance of the proposed scheme is evaluated at low error rates by a mixed simulation-analytic method. It is shown that the proposed scheme exhibits highly favorable performance vs. complexity tradeoffs compared to the other schemes.

Transmission of Visual Data over Wireless Fading Channel in Real-Time Systems Based on Superposition Coding Scheme

Real-time visual applications are among the most important requirements in the next generation wireless communication systems. In these applications, the transmitted data comprise different layers with different importance levels based on their influence on the reception quality. Furthermore, the real-time transmission nature of these applications makes them sensitive to data losses and transmission delay. To address these issues, an efficient superposition adaptive modulation and coding system, for the optimal system performance, is proposed in this paper. The proposed system switches its modulation and coding scheme adaptively to select the suitable modulation order and coding rate that best match with the instantaneous channel condition. The channel state information is estimated in receiver and fed back to transmitter. In such method, better performances in both data rate and bit error rate (BER) can be attained. Here, the source data are divided into different priority layers with different importance. Each layer bit stream is sent with specific error protection level against channel corruption. The highest error protection level is assigned to the highest priority layer, and vice versa. The modulated bit streams of all layers are then superimposed together and transmitted via Rayleigh fading channel. At the receiver side, a specific multi-stage decoding receiver is used to reconstruct the source data which demodulates the layers in the order of their priorities. Simulation results show that the proposed system provides up to 18 dB SNR and 46 % data rate gains, respectively, compared to the traditional BPSK scheme at BER of 10−4.

A Class of Nonbinary LDPC Codes with Fast Encoding and Decoding Algorithms

This letter is concerned with a class of nonbinary low-density parity-check (LDPC) codes, referred to as column-scaled LDPC (CS-LDPC) codes, whose parity-check matrices have a property that each column is a scaled binary vector. The CS-LDPC codes, which include algebraically constructed nonbinary LDPC codes as subclasses, admit fast encoding and decoding algorithms. Specifically, for a code over the finite field F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2p</sub> , the encoder can be implemented with p parallel binary LDPC encoders followed by a series of bijective mappers, while the decoder can be implemented with an iterative decoder in which no message permutations are required during the iterations. In addition, there exist low-complexity iterative multistage decoders that can be utilized to trade off the performance against the complexity. Simulation results show that the performance degradation caused by the iterative multistage decoding algorithms is relevant to the code structure.

Doubly multistage decoding of low-density parity-check codes over ℤ 2 m

A doubly multistage decoder (DMD) for low-density parity-check codes over ℤ2m, m&gt;1, which fuses the multistage decoding approaches of Armand et al. and Varnica et al., is proposed. Two variants of the DMD are considered. The first (respectively, second) performs belief-propagation (BP) [respectively, offset min-sum (OMS)] decoding in each decoding stage and is referred to as DMD - BP (respectively, DMD - OMS). For the moderate-length codes considered in this study, the computer simulations show the DMD - BP (respectively, DMD - OMS) achieving coding gains of up to 0.43 dB (respectively, 0.67 dB) over standard BP decoding at a bit error rate of 10−6 on an additive-white-Gaussian-noise channel, while requiring significantly less computational power. Remarkably, DMD - OMS outperforms DMD - BP, yet has lower computational complexity than DMD - BP. Snapshots of the log-likelihood ratio densities of the decoded bits midway through the decoding process explain the superiority of the DMD over standard BP decoding.

Low Complexity Demapping Algorithms for Multilevel Codes

In order to reduce the computational complexity of maximum-likelihood symbol estimation (MLSE) demapping of multilevel codes which is based on block partitioning and which produces soft input for a multistage decoding (MSD) process, three different demapping algorithms are proposed. It is theoretically proven that the proposed algorithms can reduce exponentially increasing computational complexity of the MLSE demapping algorithm to a constant complexity (neglecting comparisons). It is shown by extensive simulations for AWGN and Rayleigh fading channels that the proposed low complexity demapping algorithms can achieve near MLSE performance.

Multi-Stage Decoding Scheme with Post-Processing for LDPC Codes to Lower the Error Floors

In this letter, we propose a multi-stage decoding scheme with post-processing for low-density parity-check (LDPC) codes, which remedies the rapid performance degradation in the high signal-to-noise ratio (SNR) range known as error floor. In the proposed scheme, the unsuccessfully decoded words of the previous decoding stage are re-decoded by manipulating the received log-likelihood ratios (LLRs) of the properly selected variable nodes. Two effective criteria for selecting the probably erroneous variable nodes are also presented. Numerical results show that the proposed scheme can correct most of the unsuccessfully decoded words of the first stage having oscillatory behavior, which are regarded as a main cause of the error floor.

Signal Shaping for Bit-Interleaved Coded Modulation on the AWGN Channel

In this paper a coded modulation method for the additive white Gaussian noise channel is presented which incorporates signal shaping. The scheme uses a modulation map to map bits to channel inputs. A modulation map is considered that has the advantage it is can easily be combined with binary error-correcting codes. The decoding strategy is a combination of bit-interleaved coded modulation and multistage decoding. The number of required decoding stages is only small compared to other multistage decoding schemes for coded modulation. It is shown that modulation maps can be designed with a constrained capacity limit very close to the capacity of the AWGN channel. When combined with low-density parity-check codes, simulation results show that a near-capacity performance is achieved for high spectral efficiencies.

Multilevel LDPC-Coded High-Speed Optical Systems: Efficient Hard Decoding and Code Optimization

We consider a multilevel coding scheme employing low-density parity-check (LDPC) codes and high-order modulations for high-speed optical transmissions, where the coherent receiver performs either parallel independent decoding (PID) or multistage decoding (MSD). To meet the severe complexity constraint imposed by the ultrahigh data rate of the emerging optical transmission systems, we focus on hard-decision decoding of LDPC codes. A new LDPC hard decoding method is developed, which is equivalent to the Gallager decoding algorithm B, but is more efficient in terms of circuit implementation, since no variable node degree information is needed. Two variants of this decoder is also proposed, which offers significant performance gain for finite-length codes. We optimize the system by allocating rates and designing profiles for component codes. Both numerical evaluations and simulation results show that the optimized multilevel coding systems with either PID or MSD substantially outperform the optimized single-level LDPC-coded system.