Linear error correcting codes with anytime reliability

Sukhavasi, Ravi Teja; Hassibi, Babak

doi:10.1109/isit.2011.6033847

Cited by 26 publications

(21 citation statements)

References 13 publications

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“…Hence in the second step, we introduce a separate layer of parity-checks to further protect these sub-packets. The channel packet at time is modified to be: (10) where , and are obtained as in the MS construction in Section II-C, whereas is a parity-check packet generated by applying a -MDS code to the sub-packets of rate . Fig.…”

Section: Maximum Distance and Span Codesmentioning

confidence: 99%

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Streaming Codes With Partial Recovery Over Channels With Burst and Isolated Erasures

Badr

Khisti

Tan

et al. 2015

IEEE J. Sel. Top. Signal Process.

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We study forward error correction codes for low-delay, real-time streaming communication over packet erasure channels. Our encoder operates on a stream of source packets in a sequential fashion, and the decoder must output each packet in the source stream within a fixed delay. We consider a class of practical channel models with correlated erasures and introduce new "streaming codes" for efficient error correction over these channels. For our analysis, we propose a simplified class of erasure channels that introduce both burst and isolated erasures within the same decoding window. We demonstrate that the previously proposed streaming codes can lead to significant number of packet losses over such channels. Our proposed constructions involve a layered coding approach, where a burst-erasure code is first constructed, and additional layers of parity-checks are concatenated to recover from the isolated erasure patterns. We also introduce another construction that requires a significantly smaller field-size and decoding complexity, but incurs some performance loss. Numerical simulations over the Gilbert-Elliott and Fritchman channel models indicate that by addressing patterns involving both burst and isolated erasures within the same window, our proposed codes achieve significant gains over previously proposed streaming codes.Index Terms-Application layer forward error correction (AL-FEC), burst and isolated errors, Gilbert-Elliott channels, low-delay codes, real-time streaming communication.

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Section: Maximum Distance and Span Codesmentioning

confidence: 99%

“…Secondly, unlike [5], our codes only guarantee partial recovery for certain erasure patterns. For other related work on real-time streaming, see [8]- [10].…”

mentioning

confidence: 99%

Streaming Codes With Partial Recovery Over Channels With Burst and Isolated Erasures

Badr

Khisti

Tan

et al. 2015

IEEE J. Sel. Top. Signal Process.

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“…According to Lemmas 2 and 3, the end-to-end distortion is upper bounded as Substituting θ = 1/N in (24) gives…”

Section: Appendixmentioning

confidence: 99%

Dynamic source–channel coding for estimation and control over binary symmetric channels

Shirazinia

Zaidi

Bao

et al. 2015

IET Control Theory & Applications

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The authors study causal dynamic source-channel codes for mean-square stabilisation of a linear plant with random initial state, over binary symmetric channels (BSCs). A binary expansion source coding scheme and two types of channel coding schemes are investigated: (i) dynamic repetition encoding under sequential majority logic decoding, and (ii) dynamic Fountain encoding under sequential BP decoding. The coding schemes are first analysed for an openloop system, where the goal is to transmit a real-valued source over BSCs with the objective of minimising end-to-end mean-square error distortion. They derive upper-and lower bounds on the achievable distortion which is a function of time. Based on these distortion bounds, they show that the dynamic Fountain codes are able to stabilise (in mean-square sense) an unstable linear plant over BSCs. IntroductionRecent advances in sensor technology, low-power electronics, digital communications and networking have enabled the engineering of a completely new type of networked monitoring and control systems, which have the potential to drastically decrease costs and increase productivity in a wide range of industrial applications. Such systems are known as networked control systems (NCS), consisting of a plant and a group of sensors, controllers and actuators that need to exchange information over communication links to perform coordinated actions. In practice, the communication links are noisy and the transmission errors are inevitable, affecting the performance of NCS. Traditionally, long block codes are used in the design of communication systems to provide reliable communication over noise corrupted channels. However, the use of longer codes incurs larger delays in the decoding of the transmitted information, which may not be suitable for certain delay sensitive closed-loop control applications. Thus, it is important to develop delay-efficient coding methods that can be used for transmitting information within NCS. This paper makes an effort in this direction by studying delay-efficient source-channel coding methods for state estimation or stabilisation of a plant that is connected to a controller via a noisy digital communication channel. In the following, we first introduce the system model and the objectives in Section 1.1, then provide a review of the relevant literature in Section 1.2 and finally highlight the main contributions of this paper in Section 1.3. System modelConsider a discrete-time linear system (plant) with the following state equationwhere X (t) ∈ R n is a state variable and U (t) ∈ R is a control variable. The matrices A and B are of appropriate dimensions and the pair (A, B) is controllable. Let {a 1 , a 2 , . . . , a n } denote the eigenvalues of A. Without loss of generality we assume that all the eigenvalues of A are outside the unit disc, that is, |a i | ≥ 1. The unstable modes can be decoupled from the stable modes by a similarity transformation. If the system in (1) is one-dimensional then A is scalar and we use the notation A = a. We assume th...

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“…For user-j (j 2 fA, Bg), the error probability of the message i at time t is, that is, P e j .i, t/ is given in (7). || Correction added on 13 November 2015, after first online publication: equation has been corrected.…”

Section: Anytime Transmission Over Gaussian Macmentioning

confidence: 99%

“…However, these codes are not suitable for practical implementation. Practical anytime reliable transmissions for the P2P case were studied in [4][5][6][7][8][9][10]. In contrast to the P2P case, several works including [11][12][13] study anytime codes for the three terminal relay network.…”

Section: Introductionmentioning

confidence: 99%

Delay‐universal codes for multiple access channels

Noor-A-Rahim

Nguyen

Lechner

2015

Trans. Emerging Tel. Tech.

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In this paper, we propose delay‐universal or ‘anytime’ code design for multiple access channels. The anytime characteristics of the proposed coding scheme are investigated asymptotically over two different multiple access channels. For the simplest multiple access channel, we derive the analytical delay‐exponent of the proposed code by using mathematical induction technique. Through comparison, we show that the analytical delay‐exponent matches with the delay‐exponent obtained from numerical results. Copyright © 2015 John Wiley & Sons, Ltd.

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Linear error correcting codes with anytime reliability

Cited by 26 publications

References 13 publications

Streaming Codes With Partial Recovery Over Channels With Burst and Isolated Erasures

Streaming Codes With Partial Recovery Over Channels With Burst and Isolated Erasures

Dynamic source–channel coding for estimation and control over binary symmetric channels

Delay‐universal codes for multiple access channels

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