Low Decoding Complexity Research Articles

Continuous Phase Modulation and Space-Time Coding: A Candidate for Wireless Robotics

The physical layer(s) of wireless robotics take advantage of current standards, like Bluetooth, Wifi, etc., each of them addressing a specific segment of wireless robotics. Wireless robotics has a wide range of needs, comprising low power, robustness and high data rate when video is used as well as the opportunity to use a large number of transceivers. To cover these needs and take benefit from these opportunities, we propose a new physical layer, based on continuous phase modulation (CPM) and space-time coding. CPM, already used in some standards like GSM and Bluetooth, enables the development of low power devices, but presents a low spectral efficiency. Space-time coding on the other hand yields high spectral efficiency as well as enhanced robustness against the wireless channel. Moreover, space-time coding can take benefit of the large number of transceivers using cooperative communications. In this paper, after analysing the opportunities given by wireless robotics as well as its specific needs, we propose a new physical layer based on L 2-orthogonality for non-linear space-time codes. L 2-orthogonality of our codes is ensured by a bank of phase correction functions, maintaining phase continuity, but at the same time enabling low complexity decoding. We show that the code achieves full diversity and has full rate, for any number of transmit/receive antennas and any CPM parameter.

Space-Time Processing for X Channels Using Precoders

In this paper, we investigate how to send space-time codes with full diversity and low decoding complexity for X channels using precoders. First, we assume that we have 2 transmitters and 2 receivers. Each transmitter sends different codewords to each receiver at the same time. We propose an orthogonal transmission scheme that combines space-time block coding and array processing to achieve low-complexity decoding and full diversity for transmitted signals. To our best knowledge, this is the first scheme which can achieve low-complexity decoding and full diversity for any transmitted codeword in X channel when all the users transmit at the same time. Finally, we show that under certain conditions, our proposed scheme can be extended to a general case with any number of transmitters and receivers each with any number of antennas. Simulation results validate our theoretical analysis.

Array Processing for Multi-User Multi-Antenna Interference Channels Using Precoders

In this paper, we investigate how to send space-time codes with full diversity and low decoding complexity for interference channels using precoders. We assume that we have two transmitters and two receivers. Each transmitter sends codewords to respective receiver at the same time. We propose an orthogonal transmission scheme that combines space-time codes and array processing to achieve low-complexity decoding and full diversity for transmitted signals. To our best knowledge, this is the first scheme which can achieve low-complexity decoding and full diversity for any transmitted codeword in interference channel when all the users transmit at the same time. Simulation results validate our theoretical analysis.

High-Throughput Interpolator Architecture for Low-Complexity Chase Decoding of RS Codes

In this paper, a high-throughput interpolator architecture for soft-decision decoding of Reed-Solomon (RS) codes based on low-complexity chase (LCC) decoding is presented. We have formulated a modified form of the Nielson's interpolation algorithm, using some typical features of LCC decoding. The proposed algorithm works with a different scheduling, takes care of the limited growth of the polynomials, and shares the common interpolation points, for reducing the latency of interpolation. Based on the proposed modified Nielson's algorithm we have derived a low-latency architecture to reduce the overall latency of the whole LCC decoder. An efficiency of at least 39%, in terms of area-delay product, has been achieved by an LCC decoder, by using the proposed interpolator architecture, over the best of the previously reported architectures for an RS(255,239) code with eight test vectors. We have implemented the proposed interpolator in a Virtex-II FPGA device, which provides 914 Mb/s of throughput using 806 slices.

A (64,45) Triple Error Correction Code for Memory Applications

Memories are commonly protected with error correction codes to avoid data corruption when a soft error occurs. Traditionally, per-word single error correction (SEC) codes are used. This is because they are simple to implement and provide low latency. More advanced codes have been considered, but their main drawback is the complexity of the decoders and the added latency. Recently, the use of one-step majority logic decodable codes has been proposed for memory protection. One-step majority logic decoding enables the use of low-complexity decoders, and low latency can also be achieved with moderate complexity. The main issue is that there are only a few codes that are one-step majority logic decodable. This restricts the choice of word lengths and error correction capabilities. In this paper, a method to derive new codes from a class of one-step majority logic decodable codes known as difference-set codes is proposed. The derived codes can also be efficiently implemented. As an example, a (64,45) triple error correction (TEC) code is derived and compared with existing SEC and TEC codes. The results presented enable a wider choice of word lengths and error correction capabilities that will be useful for memory designs.

Two Designs of Space-Time Block Codes Achieving Full Diversity With Partial Interference Cancellation Group Decoding

A partial interference cancellation (PIC) group decoding based space-time block code (STBC) design criterion was recently proposed by Guo and Xia, where the decoding complexity and the code rate traeoff is dealt when the full diversity is achieved. In this paper, two designs of STBC are proposed for any number of transmit antennas that can obtain full diversity when a PIC group decoding (with a particular grouping scheme) is applied at receiver. With the PIC group decoding and an appropriate grouping scheme for the decoding, the proposed STBC are shown to obtain the same diversity gain as the ML decoding, but have a low decoding complexity. The first proposed STBC is designed with multiple diagonal layers and it can obtain the full diversity for two-layer design with the PIC group decoding and the rate is up to 2 symbols per channel use. With PIC-SIC group decoding, the first proposed STBC can obtain full diversity for any number of layers and the rate can be full. The second proposed STBC can obtain full diversity and a rate up to 9/4 with the PIC group decoding. Some code design examples are given and simulation results show that the newly proposed STBC can well address the rate-performance-complexity tradeoff of the MIMO systems.

Rateless Coding for Gaussian Channels

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.

Multiple Beamforming with Perfect Coding

Perfect Space-Time Block Codes (PSTBCs) achieve full diversity, full rate, nonvanishing constant minimum determinant, uniform average transmitted energy per antenna, and good shaping. However, the high decoding complexity is a critical issue for practice. When the Channel State Information (CSI) is available at both the transmitter and the receiver, Singular Value Decomposition (SVD) is commonly applied for a Multiple-Input Multiple-Output (MIMO) system to enhance the throughput or the performance. In this paper, two novel techniques, Perfect Coded Multiple Beamforming (PCMB) and Bit-Interleaved Coded Multiple Beamforming with Perfect Coding (BICMB-PC), are proposed, employing both PSTBCs and SVD with and without channel coding, respectively. With CSI at the transmitter (CSIT), the decoding complexity of PCMB is substantially reduced compared to a MIMO system employing PSTBC, providing a new prospect of CSIT. Especially, because of the special property of the generation matrices, PCMB provides much lower decoding complexity than the state-of-the-art SVD-based uncoded technique in dimensions 2 and 4. Similarly, the decoding complexity of BICMB-PC is much lower than the state-of-the-art SVD-based coded technique in these two dimensions, and the complexity gain is greater than the uncoded case. Moreover, these aforementioned complexity reductions are achieved with only negligible or modest loss in performance.

Performance improvement of QO-STBC over time-selective channel for wireless network

Signal detection for vehicle-to-vehicle and wireless network application has motivated new design for conditions in which channel is time-selective fading. Since the physical layer (PHY) forms the foundation of the communication protocol stack, the performance of this layer affects all high layers of the system stack. Quasi-orthogonal space-time block code (QO-STBC) can provide full rate transmission and partial diversity under low decoding complexity. Previous papers on QO-STBC assume that the channels are slow fading or remain static over the length of the codeword. However, time-selective channels do exist, and in this case, the decoder proposed in Jafarkhani (2001) cannot be used to achieve a proper error performance. In order to mitigate the severe performance degradation, the zero forcing (ZF) and minimum mean square error (MMSE) decoders are employed in this paper. We also propose a zero forcing interference cancellation decision-feedback equalizer (ZF-IC-DFE) and a minimum mean-square error interference cancellation decision-feedback equalizer (MMSE-IC-DFE) via Cholesky factorization of the channel Gram matrix after performing interference cancellation. By feeding back past decisions on previously detected symbols, DFE schemes can achieve an additional performance gain compared to their corresponding linear decoders.

Power-efficient decoder implementation based on state transparent convolutional codes

In this study, a power-efficient very large-scale integration (VLSI) implementation for the convolutional code decoder is presented. Based on the state transparent convolutional code definition, the receiving codewords are classified into non-erroneous and erroneous segments separately. Different from the conventional Viterbi decoder (VD), the authors use a low-complexity decoder, denoted as bit reverse decoder, to recover the non-erroneous segments using reverse operation with a little power consumption and present the segment-based VD to decode the erroneous codeword segments. Then, the clock-gating technique is employed to switch between segment-based VD and bit reverse decoder for power saving. To further reduce the power consumption, the authors group registers into several segments in the survivor memory unit of the segment-based VD and also apply clock gating to each segment individually. According to the number of consecutive erroneous codeword segments, the corresponding numbers of register segments in the survivor memory unit are enabled and other register segments are clock-gated to reduce the switching activities. Besides, our design determines the start and terminal states of the survivor path to obtain correct results of erroneous segments without bit-error rate degradation. As compared with other decoders, our design requires less power without decreasing the decoding performance.

Modulation Diversity in Fading Channels with a Quantized Receiver

In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at the receiver. With an unquantized receiver, coding based on algebraic rotations is known to achieve maximum modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee gains in diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum modulation diversity with a low-complexity minimum distance decoder and perfect channel knowledge. Relaxing the perfect channel knowledge assumption we propose a novel channel training/estimation technique to estimate the channel. We show that our coding/training/estimation scheme and minimum distance decoding achieves an error probability performance similar to that achieved with perfect channel knowledge.

L2-Orthogonal ST-Code Design for CPM

Non-linear modulations, like the Continuous phase modulation (CPM) with its constant envelope property, have been appealing for energy efficient communication systems. In parallel, linear orthogonal Space-Time block codes (STBC) have emerged as a simple way of achieving spectral efficiency by full diversity and simple decoupled maximum-likelihood decoding. However, linear codes rely on pointwise orthogonality which leads to a well-known degradation of data rate for more than two antennas. In this paper, we introduce the concept of L2-orthogonality for non-linear Space-Time codes (STC). Our approach generalizes code design based on pointwise orthogonality. Namely, we are able to derive new codes with the same advantages as pointwise orthogonal STBC, i.e. low decoding complexity and diversity gain. At the same time, we are no longer limited by the restrictions of pointwise orthogonal codes, i.e. the reduction in data rate. Actually, we show how to construct full rate codes for any arbitrary number of transmit antennas. More precisely, a family of codes for continuous phase modulation (CPM) is detailed. The L2-orthogonality of these codes is ensured by a bank of phase correction functions which maintains the phase continuity but also introduces frequency offsets. We prove that these codes achieve full diversity and have full rate. Moreover, these codes don't put any restriction on the CPM parameters.

A novel framework of online network coding for multicast switches with constrained buffers

Network coding is able to address output conflicts when fanout splitting is allowed for multicast switching. Hence, it successfully achieves a larger rate region than non-coding approaches in crossbar switches. However, network coding requires large coding buffers and a high computational cost on encoding and decoding. In this paper, we propose a novel Online Network Coding framework called Online NC for multicast switches, which is adaptive to constrained buffers. Moreover, it enjoys a much lower decoding complexity O(n 2) by a Vandermonde matrix based approach, as compared to conventional randomized network coding O(n 3). Our approach realizes online coding with one coding algorithm that synchronizes buffering and coding. Therefore, we significantly reduce requirements on buffer space, while also sustaining high throughputs. We confirm the superior advantages of our contributions using empirical studies.

Collocated and Distributed STBCs with Partial Interference Cancellation Decoding, Part I: Full-Diversity Criterion

Low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, were given by Guo and Xia along with sufficient conditions for a Space-Time Block Code (STBC) to achieve full diversity with PIC/PIC-SIC decoding for point-to-point MIMO channels. In Part-I of this two part series of papers, we give new conditions for an STBC to achieve full diversity with PIC and PIC-SIC decoders, which are equivalent to Guo and Xia's conditions, but are much easier to check. We then show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks and give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders. In Part-II, we construct new low complexity full-diversity PIC/PIC-SIC decodable STBCs and DSTBCs that achieve higher rates than the known full-diversity low complexity ML decodable STBCs and DSTBCs.

Collocated and Distributed STBCs with Partial Interference Cancellation Decoding, Part II: Code Construction

In this second part of a two part series of papers, we construct a new class of Space-Time Block Codes (STBCs) for point-to-point MIMO channel and Distributed STBCs (DSTBCs) for the amplify-and-forward relay channel that give full-diversity with Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC) decoders. The proposed class of STBCs include most of the known full-diversity low complexity PIC/PIC-SIC decodable STBCs as special cases. We also show that a number of known full-diversity PIC/PIC-SIC decodable STBCs that were constructed for the point-to-point MIMO channel can be used as full-diversity PIC/PIC-SIC decodable DSTBCs in relay networks. For the same decoding complexity, the proposed STBCs and DSTBCs achieve higher rates than the known low decoding complexity codes. Simulation results show that the new codes have a better bit error rate performance than the low ML decoding complexity codes available in the literature.

A 2x2 Shape-Preserving ST Code for UWB Communications with Multipulse PPM

In this paper, we consider the application of Multipulse Pulse Position Modulation (MPPM) as a power-efficient modulation scheme for Impulse-Radio Ultra-Wideband (IR-UWB) communications and we propose the first known MPPM-specific 2×2 space-time code that is convenient for this modulation. The proposed rate-1 code achieves a full transmit diversity order with all MPPM constellations without introducing any constellation expansion. We also show that the proposed code profits from a low decoding complexity in the absence of interference between the different modulated UWB pulses.

Decoding of the (31, 16, 7) quadratic residue code with four-error correcting capability

A high-speed algorithm for decoding the binary (31, 16, 7) quadratic residue (QR) code up to four errors is proposed. Core to the key idea lies in an innovative integration of the reliability-search procedure and the insight of the weight distribution of the code for searching the candidate codewords. Accordingly, the maximum-likelihood (ML) criterion is applied to pick the most possible codeword. Through simulation over the additive white Gaussian noise (AWGN) channel, it is concluded that the error-correcting performance of the new decoder is superior to that of a Chase-II decoder when no more than four errors occur. The overall bit error rate (BER) of the proposed decoder is close to that of the Chase-II decoder. More importantly, the new decoder results in great reductions of 72.34% and 92.37% in the signal-to-noise ratio (SNR) values of 0 and 7, respectively. The proposed algorithm suggests an alternative to enhance the error-correcting capability of the hard-decision decoder, but with a lower decoding complexity.

Mismatched Bit-Interleaved Coded Noncoherent Orthogonal Modulation

We consider several low-complexity decoding metrics for bit-interleaved coded modulation (BICM) with orthogonal signaling and noncoherent detection. Using the generalized mutual information (GMI) as the relevant performance measure, we demonstrate that only a small performance degradation is entailed by using these mismatched metrics instead of the maximum likelihood (matched) metric. Furthermore, for coded transmission with sum-product symbol-by-symbol (SBS) decoding, we illustrate that metric scaling with a constant factor can improve the throughput performance of these metrics.

High-Rate and Full-Diversity Space-Time Block Codes with Low Complexity Partial Interference Cancellation Group Decoding

In this letter, we propose a systematic design of space-time block codes (STBC) which can achieve high rate and full diversity when the partial interference cancellation (PIC) group decoding is used at receivers. The proposed codes can be applied to any number of transmit antennas and admit a low decoding complexity while achieving full diversity. For M transmit antennas, in each codeword real and imaginary parts of PM complex information symbols are parsed into P diagonal layers and then encoded, respectively. With PIC group decoding, it is shown that the decoding complexity can be reduced to a joint decoding of M/2 real symbols. In particular, for 4 transmit antennas, the code has real symbol pairwise (i.e., single complex symbol) decoding that achieves full diversity and the code rate is 4/3. Simulation results demonstrate that the full diversity is offered by the newly proposed STBC with the PIC group decoding.

Distributed Video Coding: CODEC Architecture and Implementation

Distributed Video Coding (DVC) is a new coding paradigm for video compression, based on Slepian- Wolf (lossless coding) and Wyner-Ziv (lossy coding) information theoretic results. DVC is useful for emerging applications such as wireless video cameras, wireless low-power surveillance networks and disposable video cameras for medical applications etc. The primary objective of DVC is low-complexity video encoding, where bulk of computation is shifted to the decoder, as opposed to low-complexity decoder in conventional video compression standards such as H.264 and MPEG etc. There are couple of early architectures and implementations of DVC from Stanford University[2][3] in 2002, Berkeley University PRISM (Power-efficient, Robust, hIgh-compression, Syndrome-based Multimedia coding)[4][5] in 2002 and European project DISCOVER (DIStributed COding for Video SERvices)[6] in 2007. Primarily there are two types of DVC techniques namely pixel domain and transform domain based. Transform domain design will have better rate-distortion (RD) performance as it exploits spatial correlation between neighbouring samples and compacts the block energy into as few transform coefficients as possible (aka energy compaction). In this paper, architecture, implementation details and "C" model results of our transform domain DVC are presented.