arXiv subjects

B. Sundar Rajan

Publications and source records attributed to B. Sundar Rajan.

At least 199 records · Page 11Linked to original sources

arXiv2010

Reduced ML-Decoding Complexity, Full-Rate STBCs for 4 Transmit Antenna Systems

For an $n_t$ transmit, $n_r$ receive antenna system ($n_t \times n_r$ system), a {\it{full-rate}} space time block code (STBC) transmits $min(n_t,n_r)$ complex symbols per channel use. In this paper, a scheme to obtain a full-rate STBC for 4 transmit antennas and any $n_r$, with reduced ML-decoding complexity is presented. The weight matrices of the proposed STBC are obtained from the unitary matrix representations of Clifford Algebra. By puncturing the symbols of the STBC, full rate designs can be obtained for $n_r < 4$. For any value of $n_r$, the proposed design offers the least ML-decoding complexity among known codes. The proposed design is comparable in error performance to the well known perfect code for 4 transmit antennas while offering lower ML-decoding complexity. Further, when $n_r < 4$, the proposed design has higher ergodic capacity than the punctured Perfect code. Simulation results which corroborate these claims are presented.

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arXiv2010

On Network-Error Correcting Convolutional Codes under the BSC Edge Error Model

Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the performance of CNECCs under the error model of the network where the edges are assumed to be statistically independent binary symmetric channels, each with the same probability of error $p_e$($0\leq p_e<0.5$). We obtain bounds on the performance of such CNECCs based on a modified generating function (the transfer function) of the CNECCs. For a given network, we derive a mathematical condition on how small $p_e$ should be so that only single edge network-errors need to be accounted for, thus reducing the complexity of evaluating the probability of error of any CNECC. Simulations indicate that convolutional codes are required to possess different properties to achieve good performance in low $p_e$ and high $p_e$ regimes. For the low $p_e$ regime, convolutional codes with good distance properties show good performance. For the high $p_e$ regime, convolutional codes that have a good \textit{slope} (the minimum normalized cycle weight) are seen to be good. We derive a lower bound on the slope of any rate $b/c$ convolutional code with a certain degree.

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arXiv2010

Orthogonal vs Non-Orthogonal Multiple Access with Finite Input Alphabet and Finite Bandwidth

For a two-user Gaussian multiple access channel (GMAC), frequency division multiple access (FDMA), a well known orthogonal-multiple-access (O-MA) scheme has been preferred to non-orthogonal-multiple-access (NO-MA) schemes since FDMA can achieve the sum-capacity of the channel with only single-user decoding complexity [\emph{Chapter 14, Elements of Information Theory by Cover and Thomas}]. However, with finite alphabets, in this paper, we show that NO-MA is better than O-MA for a two-user GMAC. We plot the constellation constrained (CC) capacity regions of a two-user GMAC with FDMA and time division multiple access (TDMA) and compare them with the CC capacity regions with trellis coded multiple access (TCMA), a recently introduced NO-MA scheme. Unlike the Gaussian alphabets case, it is shown that the CC capacity region with FDMA is strictly contained inside the CC capacity region with TCMA. In particular, for a given bandwidth, the gap between the CC capacity regions with TCMA and FDMA is shown to increase with the increase in the average power constraint. Also, for a given power constraint, the gap between the CC capacity regions with TCMA and FDMA is shown to decrease with the increase in the bandwidth. Hence, for finite alphabets, a NO-MA scheme such as TCMA is better than the well known O-MAC schemes, FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for a two-user GMAC.

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arXiv2009

Near-ML Signal Detection in Large-Dimension Linear Vector Channels Using Reactive Tabu Search

Low-complexity near-optimal signal detection in large dimensional communication systems is a challenge. In this paper, we present a reactive tabu search (RTS) algorithm, a heuristic based combinatorial optimization technique, to achieve low-complexity near-maximum likelihood (ML) signal detection in linear vector channels with large dimensions. Two practically important large-dimension linear vector channels are considered: i) multiple-input multiple-output (MIMO) channels with large number (tens) of transmit and receive antennas, and ii) severely delay-spread MIMO inter-symbol interference (ISI) channels with large number (tens to hundreds) of multipath components. These channels are of interest because the former offers the benefit of increased spectral efficiency (several tens of bps/Hz) and the latter offers the benefit of high time-diversity orders. Our simulation results show that, while algorithms including variants of sphere decoding do not scale well for large dimensions, the proposed RTS algorithm scales well for signal detection in large dimensions while achieving increasingly closer to ML performance for increasing number of dimensions.

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arXiv2009

Asymptotic Analysis of the Performance of LAS Algorithm for Large-MIMO Detection

In our recent work, we reported an exhaustive study on the simulated bit error rate (BER) performance of a low-complexity likelihood ascent search (LAS) algorithm for detection in large multiple-input multiple-output (MIMO) systems with large number of antennas that achieve high spectral efficiencies. Though the algorithm was shown to achieve increasingly closer to near maximum-likelihood (ML) performance through simulations, no BER analysis was reported. Here, we extend our work on LAS and report an asymptotic BER analysis of the LAS algorithm in the large system limit, where $N_t,N_r \to \infty$ with $N_t=N_r$, where $N_t$ and $N_r$ are the number of transmit and receive antennas. We prove that the error performance of the LAS detector in V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the ML detector as $N_t,N_r \to \infty$.

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arXiv2009

High-Rate Space-Time Coded Large MIMO Systems: Low-Complexity Detection and Channel Estimation

In this paper, we present a low-complexity algorithm for detection in high-rate, non-orthogonal space-time block coded (STBC) large-MIMO systems that achieve high spectral efficiencies of the order of tens of bps/Hz. We also present a training-based iterative detection/channel estimation scheme for such large STBC MIMO systems. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed multistage likelihood ascent search (M-LAS) detector in conjunction with the proposed iterative detection/channel estimation scheme at low complexities. The fact that we could show such good results for large STBCs like 16x16 and 32x32 STBCs from Cyclic Division Algebras (CDA) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding) establishes the effectiveness of the proposed detector and channel estimator. We decode perfect codes of large dimensions using the proposed detector. With the feasibility of such a low-complexity detection/channel estimation scheme, large-MIMO systems with tens of antennas operating at several tens of bps/Hz spectral efficiencies can become practical, enabling interesting high data rate wireless applications.

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arXiv2009

Training-Embedded, Single-Symbol ML-Decodable, Distributed STBCs for Relay Networks

Recently, a special class of complex designs called Training-Embedded Complex Orthogonal Designs (TE-CODs) has been introduced to construct single-symbol Maximum Likelihood (ML) decodable (SSD) distributed space-time block codes (DSTBCs) for two-hop wireless relay networks using the amplify and forward protocol. However, to implement DSTBCs from square TE-CODs, the overhead due to the transmission of training symbols becomes prohibitively large as the number of relays increase. In this paper, we propose TE-Coordinate Interleaved Orthogonal Designs (TE-CIODs) to construct SSD DSTBCs. Exploiting the block diagonal structure of TE-CIODs, we show that, the overhead due to the transmission of training symbols to implement DSTBCs from TE-CIODs is smaller than that for TE-CODs. We also show that DSTBCs from TE-CIODs offer higher rate than those from TE-CODs for identical number of relays while maintaining the SSD and full-diversity properties.

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arXiv2009

Network error correction for unit-delay, memory-free networks using convolutional codes

A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the symbols received at their incoming edges on their outgoing edges. In this work, we introduce network-error correction for single source, acyclic, unit-delay, memory-free networks with coherent network coding for multicast. A convolutional code is designed at the source based on the network code in order to correct network-errors that correspond to any of a given set of error patterns, as long as consecutive errors are separated by a certain interval which depends on the convolutional code selected. Bounds on this interval and the field size required for constructing the convolutional code with the required free distance are also obtained. We illustrate the performance of convolutional network error correcting codes (CNECCs) designed for the unit-delay networks using simulations of CNECCs on an example network under a probabilistic error model.

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arXiv2009

Single-generation Network Coding for Networks with Delay

A single-source network is said to be \textit{memory-free} if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the incoming symbols (received at their incoming edges) on their outgoing edges. Memory-free networks with delay using network coding are forced to do inter-generation network coding, as a result of which the problem of some or all sinks requiring a large amount of memory for decoding is faced. In this work, we address this problem by utilizing memory elements at the internal nodes of the network also, which results in the reduction of the number of memory elements used at the sinks. We give an algorithm which employs memory at the nodes to achieve single-generation network coding. For fixed latency, our algorithm reduces the total number of memory elements used in the network to achieve single-generation network coding. We also discuss the advantages of employing single-generation network coding together with convolutional network-error correction codes (CNECCs) for networks with unit-delay and illustrate the performance gain of CNECCs by using memory at the intermediate nodes using simulations on an example network under a probabilistic network error model.

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arXiv2009

STBCs with Reduced Sphere Decoding Complexity for Two-User MIMO-MAC

In this paper, Space-Time Block Codes (STBCs) with reduced Sphere Decoding Complexity (SDC) are constructed for two-user Multiple-Input Multiple-Output (MIMO) fading multiple access channels. In this set-up, both the users employ identical STBCs and the destination performs sphere decoding for the symbols of the two users. First, we identify the positions of the zeros in the $\textbf{R}$ matrix arising out of the Q-R decomposition of the lattice generator such that (i) the worst case SDC (WSDC) and (ii) the average SDC (ASDC) are reduced. Then, a set of necessary and sufficient conditions on the lattice generator is provided such that the $\textbf{R}$ matrix has zeros at the identified positions. Subsequently, explicit constructions of STBCs which results in the reduced ASDC are presented. The rate (in complex symbols per channel use) of the proposed designs is at most $2/N_{t}$ where $N_{t}$ denotes the number of transmit antennas for each user. We also show that the class of STBCs from complex orthogonal designs (other than the Alamouti design) reduce the WSDC but not the ASDC.

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arXiv2009

Trellis Coded Modulation for Two-User Unequal-Rate Gaussian MAC

In this paper, code pairs based on trellis coded modulation are proposed over PSK signal sets for a two-user Gaussian multiple access channel. In order to provide unique decodability property to the receiver and to maximally enlarge the constellation constrained (CC) capacity region, a relative angle of rotation is introduced between the signal sets. Subsequently, the structure of the \textit{sum alphabet} of two PSK signal sets is exploited to prove that Ungerboeck labelling on the trellis of each user maximizes the guaranteed minimum squared Euclidean distance, $d^{2}_{g, min}$ in the \textit{sum trellis}. Hence, such a labelling scheme can be used systematically to construct trellis code pairs for a two-user GMAC to approach \emph{any rate pair} within the capacity region.

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arXiv2009

Convolutional Codes for Network-Error Correction

In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors are separated by a certain interval. We also give some bounds on the field size and the number of errors that can get corrected in a certain interval. Compared to previous network error correction schemes, using convolutional codes is seen to have advantages in field size and decoding technique. Some examples are discussed which illustrate the several possible situations that arise in this context.

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arXiv2009

High-Rate, Distributed Training-Embedded Complex Orthogonal Designs for Relay Networks

Distributed Space-Time Block Codes (DSTBCs) from Complex Orthogonal Designs (CODs) (both square and non-square CODs other than the Alamouti design) are known to lose their single-symbol ML decodable (SSD) property when used in two-hop wireless relay networks using amplify and forward protocol. For such a network, in this paper, a new class of high rate, training-embedded (TE) SSD DSTBCs are constructed from TE-CODs. The proposed codes include the training symbols in the structure of the code which is shown to be the key point to obtain high rate as well as the SSD property. TE-CODs are shown to offer full-diversity for arbitrary complex constellations. Non-square TE-CODs are shown to provide higher rates (in symbols per channel use) compared to the known SSD DSTBCs for relay networks with number of relays less than $10.$

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arXiv2009

Coding for Two-User SISO and MIMO Multiple Access Channels

Constellation Constrained (CC) capacity regions of a two-user SISO Gaussian Multiple Access Channel (GMAC) with finite complex input alphabets and continuous output are computed in this paper. When both the users employ the same code alphabet, it is well known that an appropriate rotation between the alphabets provides unique decodability to the receiver. For such a set-up, a metric is proposed to compute the angle(s) of rotation between the alphabets such that the CC capacity region is maximally enlarged. Subsequently, code pairs based on Trellis Coded Modulation (TCM) are designed for the two-user GMAC with $M$-PSK and $M$-PAM alphabet pairs for arbitrary values of $M$ and it is proved that, for certain angles of rotation, Ungerboeck labelling on the trellis of each user maximizes the guaranteed squared Euclidean distance of the \textit{sum trellis}. Hence, such a labelling scheme can be used systematically to construct trellis code pairs for a two-user GMAC to achieve sum rates close to the sum capacity of the channel. More importantly, it is shown for the first time that ML decoding complexity at the destination is significantly reduced when $M$-PAM alphabet pairs are employed with \textit{almost} no loss in the sum capacity. \indent A two-user Multiple Input Multiple Output (MIMO) fading MAC with $N_{t}$ antennas at both the users and a single antenna at the destination has also been considered with the assumption that the destination has the perfect knowledge of channel state information and the two users have the perfect knowledge of only the phase components of their channels. For such a set-up, two distinct classes of Space Time Block Code (STBC) pairs derived from the well known class of real orthogonal designs are proposed such that the STBC pairs are information lossless and have low ML decoding complexity.

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arXiv2009

FRFD MIMO Systems: Precoded V-BLAST with Limited Feedback Versus Non-orthogonal STBC MIMO

Full-rate (FR) and full-diversity (FD) are attractive features in MIMO systems. We refer to systems which achieve both FR and FD simultaneously as FRFD systems. Non-orthogonal STBCs can achieve FRFD without feedback, but their ML decoding complexities are high. V-BLAST without precoding achieves FR but not FD. FRFD can be achieved in V-BLAST through precoding given full channel state information at the transmitter (CSIT). However, with limited feedback precoding, V-BLAST achieves FD, but with some rate loss. Our contribution in this paper is two-fold: $i)$ we propose a limited feedback (LFB) precoding scheme which achieves FRFD in $2\times 2$, $3\times 3$ and $4\times 4$ V-BLAST systems (we refer to this scheme as FRFD-VBLAST-LFB scheme), and $ii)$ comparing the performances of the FRFD-VBLAST-LFB scheme and non-orthogonal STBCs without feedback (e.g., Golden code, perfect codes) under ML decoding, we show that in $2\times 2$ MIMO system with 4-QAM/16-QAM, FRFD-VBLAST-LFB scheme outperforms the Golden code by about 0.6 dB; in $3\times 3$ and $4\times 4$ MIMO systems, the performance of FRFD-VBLAST-LFB scheme is comparable to the performance of perfect codes. The FRFD-VBLAST-LFB scheme is attractive because 1) ML decoding becomes less complex compared to that of non-orthogonal STBCs, 2) the number of feedback bits required to achieve the above performance is small, 3) in slow-fading, it is adequate to send feedback bits only occasionally, and 4) in most practical wireless systems feedback channel is often available (e.g., for adaptive modulation, rate/power control).

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arXiv2009

Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using Reactive Tabu Search

Non-orthogonal space-time block codes (STBC) with {\em large dimensions} are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) {\em as well as} full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having large dimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of $12\times 12$ STBC from CDA and 4-QAM with 288 real dimensions achieves $i)$ $10^{-3}$ uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and $ii)$ a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS. We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlated MIMO channel model, and by using a training based iterative RTS decoding/channel estimation scheme.

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arXiv2009

Belief Propagation Based Decoding of Large Non-Orthogonal STBCs

In this paper, we present a belief propagation (BP) based algorithm for decoding non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) having {\em large dimensions}. The proposed approach involves message passing on Markov random field (MRF) representation of the STBC MIMO system. Adoption of BP approach to decode non-orthogonal STBCs of large dimensions has not been reported so far. Our simulation results show that the proposed BP-based decoding achieves increasingly closer to SISO AWGN performance for increased number of dimensions. In addition, it also achieves near-capacity turbo coded BER performance; for e.g., with BP decoding of $24\times 24$ STBC from CDA using BPSK (i.e., 576 real dimensions) and rate-1/2 turbo code (i.e., 12 bps/Hz spectral efficiency), coded BER performance close to within just about 2.5 dB from the theoretical MIMO capacity is achieved.

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arXiv2009

Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs Using PDA

Non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) having large dimensions are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) {\em as well as} full transmit diversity. Decoding of non-orthogonal STBCs with hundreds of dimensions has been a challenge. In this paper, we present a probabilistic data association (PDA) based algorithm for decoding non-orthogonal STBCs with large dimensions. Our simulation results show that the proposed PDA-based algorithm achieves near SISO AWGN uncoded BER as well as near-capacity coded BER (within about 5 dB of the theoretical capacity) for large non-orthogonal STBCs from CDA. We study the effect of spatial correlation on the BER, and show that the performance loss due to spatial correlation can be alleviated by providing more receive spatial dimensions. We report good BER performance when a training-based iterative decoding/channel estimation is used (instead of assuming perfect channel knowledge) in channels with large coherence times. A comparison of the performances of the PDA algorithm and the likelihood ascent search (LAS) algorithm (reported in our recent work) is also presented.

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