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ABSTRACT: The encoding complexity of a general (en,ek) quasi-cyclic code is
O[(e^2)(n-k)k]. This paper presents a novel low-complexity encoding algorithm
for quasi-cyclic (QC) codes based on matrix transformation. First, a message
vector is encoded into a transformed codeword in the transform domain. Then,
the transmitted codeword is obtained from the transformed codeword by the
inverse Galois Fourier transform. For binary QC codes, a simple and fast
mapping is required to post-process the transformed codeword such that the
transmitted codeword is binary as well. The complexity of our proposed encoding
algorithm is O[e(n-k)k] symbol operations for non-binary codes and
O[ek(n-k)(log_2 e)] bit operations for binary codes. These complexities are
much lower than their traditional counterpart O[(e^2)(n-k)k]. For example, our
complexity of encoding a 64-ary (4095,2160) QC code is only 1.59% of that of
traditional encoding, and our complexities of encoding the binary (4095, 2160)
and (8176, 7154) QC codes are respectively 9.52% and 1.77% of those of
traditional encoding. We also study the application of our low-complexity
encoding algorithm to one of the most important subclasses of QC codes, namely
QC-LDPC codes, especially when their parity-check matrices are rank deficient.
01/2013;
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ABSTRACT: In this work, we investigate the minimum energy of transmitting correlated
sources over the Gaussian multiple-access channel (MAC). Compared to other
works on joint source-channel coding, we consider the general scenario where
the source and channel bandwidths are not naturally matched. In particular, we
proposed the use of hybrid digital-analog coding over to improve the
transmission energy efficiency. Different models of correlated sources are
studied. We first consider lossless transmission of binary sources over the
MAC. We then treat lossy transmission of Gaussian sources over the Gaussian
MAC, including CEO sources and multiterminal sources. In all cases, we show
that hybrid transmission achieves the best known energy efficiency.
01/2013;
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Yang Yang, Zixiang Xiong
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ABSTRACT: This paper considers a distributed source coding (DSC) problem where $L$ encoders observe noisy linear combinations of $K$ correlated remote Gaussian sources, and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum-distortion constraint. This DSC problem is referred to as the generalized Gaussian CEO problem since it can be viewed as a generalization of the quadratic Gaussian CEO problem where the number of remote source $K=1$. First, we provide a new outer region obtained using the entropy power inequality and an equivalent argument (in the sense of having the same rate-distortion region and Berger–Tung inner region) among a certain class of generalized Gaussian CEO problems. We then give two sufficient conditions for our new outer region to match the inner region achieved by Berger–Tung schemes, where the second matching condition implies that in the low-distortion regime, the Berger–Tung inner rate region is always tight, while in the high-distortion regime, the same region is tight if a certain condition holds. The sum-rate part of the outer region is also studied and shown to meet the Berger–Tung sum-rate upper bound under a certain condition, which is obtained using the Karush–Kuhn–Tucker conditions of the underlying convex semidefinite optimization problem, and is in general weaker than the aforesaid two for rate region tightness.
IEEE Transactions on Information Theory - TIT. 01/2012; 58(6):3350-3372.
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ABSTRACT: It has recently been showed that lattice/structured codes can outperform random/unstructured codes in a number of scenarios of distributed source coding. One such instance involves lossy distributed compression of linear functions of Gaussian sources, which is the focus of this paper. Existing structured schemes employ “good” lattices for quantization and binning, however, the remaining correlation between the lattice coset indices are not exploited in an efficient way, leading to suboptimal performance when the target distortion is small. This paper proposes a new lattice-based scheme that is capable of eliminating the redundancy among coset indices and achieving a smaller sum-rate than existing schemes. The main novelty lies in the use of a hidden relationship between the coset planes of the quantization indices, and the enlarged set of choices for the quantizers as well as the linear estimation coefficients.
Information Theory and Applications Workshop (ITA), 2011; 03/2011
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IEEE Transactions on Signal Processing. 01/2011; 59:209-222.
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Proceedings of the Global Communications Conference, GLOBECOM 2011, 5-9 December 2011, Houston, Texas, USA; 01/2011
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ABSTRACT: In this paper, we consider cooperation in the low power (low SNR) regime for the multiple access channel with the assumption that the transmitters have no channel state information. A relevant performance measure to consider is therefore the outage capacity. We develop cooperation methods based on multiplexed coding in conjunction with rateless codes and find the achievable rates and in particular the minimum energy per bit required to achieve a certain outage probability. We consider two modes of operation: full duplex [code-division multiple access (CDMA)], where nodes can transmit and receive simultaneously on the same frequency band, and half duplex [frequency-division multiple access (FDMA)], where the nodes transmit and listen on different frequency bands. We show that, perhaps surprisingly, there is little loss in performance when using FDMA. Furthermore, our results show that multiplexed rateless codes come within 0.1 dB of the outer bound on capacity. We also develop practical rateless coding methods for FDMA using multiplexed Raptor codes which operate within 0.52 and 1.1 dB of the theoretical limit for the two- and four-user case, respectively.
IEEE Transactions on Signal Processing 10/2010; · 2.63 Impact Factor
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ABSTRACT: We consider outage capacity in the broadcast channel when the base-station has none or little channel knowledge. We find the minimum energy per bit needed to achieve a certain outage probability and the corresponding wideband slope.
Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on; 07/2010
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04/2010: pages 609 - 643; , ISBN: 9780470487068
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ABSTRACT: This work considers a distributed source coding (DSC) problem where L encoders observe noisy linear combinations of K correlated remote Gaussian sources with K ≤ L, and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum-distortion constraint. This DSC problem can be viewed as a generalization of the quadratic Gaussian CEO problem with only one remote source; it is also an extension of Oohama's latest work with correlated Gaussian remote sources, where the number of remote sources equals the number of observations. For our new DSC problem, we first provide general inner and outer rate regions, followed by a tighter outer rate region when the transform matrix between the sources and the encoders is semi-orthogonal. We then give a sufficient condition - in the form of capping the target distortion under certain threshold - for our inner and outer rate regions to match. When K = 1, both our inner and outer regions specialize to known result for the Gaussian CEO problem; with K = L and identity transform, our inner and outer regions degenerate to those provided by Oohama, however, our sufficient condition is more relaxed in the sense of allowing more matching cases.
Information Theory Workshop (ITW), 2010 IEEE; 02/2010
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IEEE International Symposium on Information Theory, ISIT 2010, June 13-18, 2010, Austin, Texas, USA, Proceedings; 01/2010
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Proceedings of IEEE International Conference on Communications, ICC 2010, Cape Town, South Africa, 23-27 May 2010; 01/2010
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Yang Yang, Yifu Zhang, Zixiang Xiong
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ABSTRACT: This work considers the quadratic Gaussian multiterminal (MT) source coding
problem and provides a new sufficient condition for the Berger-Tung sum-rate
bound to be tight. The converse proof utilizes a set of virtual remote sources
given which the MT sources are block independent with a maximum block size of
two. The given MT source coding problem is then related to a set of
two-terminal problems with matrix-distortion constraints, for which a new lower
bound on the sum-rate is given. Finally, a convex optimization problem is
formulated and a sufficient condition derived for the optimal BT scheme to
satisfy the subgradient based Karush-Kuhn-Tucker condition. The set of sum-rate
tightness problems defined by our new sufficient condition subsumes all
previously known tight cases, and opens new direction for a more general
partial solution.
Computing Research Repository - CORR. 01/2010;
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ABSTRACT: Fountain codes were introduced as an efficient and universal forward error correction (FEC) solution for data multicast over lossy packet networks. They have recently been proposed for large scale multimedia content delivery in practical multimedia distribution systems. However, standard fountain codes, such as LT or Raptor codes, are not designed to meet unequal error protection (UEP) requirements typical in real-time scalable video multicast applications. In this paper, we propose recently introduced UEP expanding window fountain (EWF) codes as a flexible and efficient solution for real-time scalable video multicast. We demonstrate that the design flexibility and UEP performance make EWF codes ideally suited for this scenario, i.e., EWF codes offer a number of design parameters to be ldquotunedrdquo at the server side to meet the different reception criteria of heterogeneous receivers. The performance analysis using both analytical results and simulation experiments of H.264 scalable video coding (SVC) multicast to heterogeneous receiver classes confirms the flexibility and efficiency of the proposed EWF-based FEC solution.
IEEE Transactions on Multimedia 11/2009; · 1.93 Impact Factor
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ABSTRACT: Slepian-Wolf (SW) coding, which is concerned with separate near-lossless compression of correlated sources (with joint decoding), forms the basis of distributed source coding (DSC) and can be used to exploit the correlation among quantized sources in lossy DSC problems such as Wyner-Ziv (WZ) coding and multiterminal (MT) source coding. However, SW coding is in general lossy, especially at short block length, and practical implementation is not nearly as well understood as entropy coding. This paper studies distributed source coding without SW coding. We employ entropy coding (after quantization if necessary) at each encoder while relying on joint estimation at the decoder to exploit the source correlation. We start from the simple lossless case before giving single-letter characterizations of the rate-distortion function for WZ coding without SW compression, and achievable rate region for MT source coding without SW compression. Examples on the binary symmetric and quadratic Gaussian cases are given.
Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009
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ABSTRACT: This paper examines near-capacity dirty-paper code designs based on source-channel coding. We first point out that the performance loss in signal-to-noise ratio (SNR) in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss, which is a function of the granular loss from source coding and the target dirty-paper coding rate (or SNR). We then examine practical designs by combining trellis-coded quantization (TCQ) with both systematic and nonsystematic irregular repeat-accumulate (IRA) codes. Like previous approaches, we exploit the extrinsic information transfer (EXIT) chart technique for capacity-approaching IRA code design; but unlike previous approaches, we emphasize the role of strong source coding to achieve as much granular gain as possible using TCQ. Instead of systematic doping, we employ two relatively shifted TCQ codebooks, where the shift is optimized (via tuning the EXIT charts) to facilitate the IRA code design. Our designs synergistically combine TCQ with IRA codes so that they work together as well as they do individually. By bringing together TCQ (the best quantizer from the source coding community) and EXIT chart-based IRA code designs (the best from the channel coding community), we are able to approach the theoretical limit of dirty-paper coding. For example, at 0.25 bit per symbol (b/s), our best code design (with 2048-state TCQ) performs only 0.630 dB away from the Shannon capacity.
IEEE Transactions on Information Theory 08/2009; · 3.01 Impact Factor
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ABSTRACT: This paper considers the problem of communicating correlated information from multiple source nodes over a network of noiseless channels to multiple destination nodes, where each destination node wants to recover all sources. The problem involves a joint consideration of distributed compression and network information relaying. Although the optimal rate region has been theoretically characterized, it was not clear how to design practical communication schemes with low complexity. This work provides a partial solution to this problem by proposing a low-complexity scheme for the special case with two sources whose correlation is characterized by a binary symmetric channel. Our scheme is based on a careful combination of linear syndrome-based Slepian-Wolf coding and random linear mixing (network coding). It is in general suboptimal; however, its low complexity and robustness to network dynamics make it suitable for practical implementation.
IEEE Transactions on Information Theory 05/2009; · 3.01 Impact Factor
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ABSTRACT: We propose a new technique, compress-spread forward (CSF), for high-performance wireless streaming from two base stations in parallel. CSF uses multiterminal source coding for efficient source compression and complete complementary sequences for error-free multiple access and synchronization. Our practical design shows significant performance gains due to spatial diversity and distributed source coding.
IEEE Transactions on Communications 05/2009; · 1.68 Impact Factor
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ABSTRACT: Recent information-theoretic results show the optimality of dirty-paper coding (DPC) in achieving the full capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). This paper presents a DPC based code design for BCs. We consider the case in which there is an individual rate/signal-to-interference-plus-noise ratio (SINR) constraint for each user. For a fixed transmitter power, we choose the linear transmit precoding matrix such that the SINRs at users are uniformly maximized, thus ensuring the best bit-error rate performance. We start with Cover's simplest two-user Gaussian BC and present a coding scheme that operates 1.44 dB from the boundary of the capacity region at the rate of one bit per real sample (b/s) for each user. We then extend the coding strategy to a two-user MIMO Gaussian BC with two transmit antennas at the base-station and develop the first limit-approaching code design using nested turbo codes for DPC. At the rate of 1 b/s for each user, our design operates 1.48 dB from the capacity region boundary. We also consider the performance of our scheme over a slow fading BC. For two transmit antennas, simulation results indicate a performance loss of only 1.4 dB, 1.64 dB and 1.99 dB from the theoretical limit in terms of the total transmission power for the two, three and four user case, respectively.
IEEE Transactions on Communications 05/2009; · 1.68 Impact Factor
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ABSTRACT: This paper considers trellis coded quantization (TCQ) and low-density parity-check (LDPC) codes for the quadratic Gaussian Wyner-Ziv coding problem. After TCQ of the source X, LDPC codes are used to implement Slepian-Wolf coding of the quantized source Q(X) with side information Y at the decoder. Assuming 256-state TCQ and ideal Slepian-Wolf coding in the sense of achieving the theoretical limit H(Q(X)|Y ), we experimentally show that Slepian-Wolf coded TCQ performs 0.2 dB away from the Wyner-Ziv distortion-rate function D<sub>WZ</sub>(R) at high rate. This result mirrors that of entropy-constrained TCQ in classic source coding of Gaussian sources. Furthermore, using 8,192-state TCQ and assuming ideal Slepian-Wolf coding, our simulations show that Slepian-Wolf coded TCQ performs only 0.1 dB away from D<sub>WZ</sub>(R) at high rate. These results establish the practical performance limit of Slepian-Wolf coded TCQ for quadratic Gaussian Wyner-Ziv coding. Practical designs give performance very close to the theoretical limit. For example, with 8,192-state TCQ, irregular LDPC codes for Slepian-Wolf coding and optimal non-linear estimation at the decoder, our performance gap to D<sub>WZ</sub>(R) is 0.20 dB, 0.22 dB, 0.30 dB, and 0.93 dB at 3.83 bit per sample (b/s), 1.83 b/s, 1.53 b/s, and 1.05 b/s, respectively. When 256-state 4-D trellis-coded vector quantization instead of TCQ is employed, the performance gap to D<sub>WZ</sub>(R) is 0.51 dB, 0.51 dB, 0.54 dB, and 0.80 dB at 2.04 b/s, 1.38 b/s, 1.0 b/s, and 0.5 b/s, respectively.
IEEE Transactions on Communications 03/2009; · 1.68 Impact Factor
