This paper revisits the problem of rate distortion optimization (RDO) with focus on inter-picture dependence. A joint RDO framework which incorporates the Lagrange multiplier as one of parameters to ...be optimized is proposed. Simplification strategies are demonstrated for practical applications. To make the problem tractable, we consider an approach where prediction residuals of pictures in a video sequence are assumed to be emitted from a finite set of sources. Consequently the RDO problem is formulated as finding optimal coding parameters for a finite number of sources, regardless of the length of the video sequence. Specifically, in cases where a hierarchical prediction structure is used, prediction residuals of pictures at the same prediction layer are assumed to be emitted from a common source. Following this approach, we propose an iterative algorithm to alternatively optimize the selections of quantization parameters (QPs) and the corresponding Lagrange multipliers. Based on the results of the iterative algorithm, we further propose two practical algorithms to compute QPs and the Lagrange multipliers for the RA(random access) hierarchical video coding: the first practical algorithm uses a fixed formula to compute QPs and the Lagrange multipliers, and the second practical algorithm adaptively adjusts both QPs and the Lagrange multipliers. Experimental results show that these three algorithms, integrated into the HM 16.20 reference software of HEVC, can achieve considerable RD improvements over the standard HM 16.20 encoder, in the common RA test configuration.
Hybrid capacitors, especially sodium-ion capacitors (SICs), which combine the complementary merits of high-energy batteries and high-power capacitors, have received increasing research interest and ...have been expected to bridge the gap between the rechargeable batteries and EDLCs. The biggest challenge for SICs is to overcome the kinetics discrepancy between the sluggish faradaic anode and the rapid nonfaradaic capacitive cathode. To boost the Na+ reaction kinetics, robust and conductive Na2Ti2O5–x nanowire arrays have been constructed as an accessible and affordable SIC anode. It is found that the utilization of oxygen vacancies (OVs) can endow Na2Ti2O5–x high electrical conductivity, introduce intercalation pseudocapacitance, and maintain the crystal structure integrity. It exhibits high reversible discharge capacity (225 mAh g–1 at 0.5C), superior rate capability, and ultralong lifespan when utilized as self-supported and additive-free anode for SIB, remaining almost 100% capacity retention after 20 000 cycles at 25 C. When assembled as flexible hybrid SIC (4.5 cm3) with rGO/AC film cathode, a high-level energy density of 70 Wh kg–1 at power density of 240 W kg–1 based on active materials can be achieved, and high volumetric energy density (15.6 Wh L–1) and power density (120 W L–1) based on the whole packge volume can be delivered with superior cycle stability (5000 cycles, 82.5%).
Pyrolytic biochar and hydrothermal biochar of corn stalk were prepared at different temperatures, and their abilities to remove iodate were compared. The characterization results show that the ...preparation temperature determines the degree of carbonization and the specific surface area of biochar. Pyrolytic biochar has a larger specific surface area than hydrothermal biochar, but retains fewer oxygen-containing functional groups. The adsorption capacity of hydrothermal biochar (16.87 mg g
−1
) is better than that of pyrolytic biochar (10.31 mg g
−1
). Corn stalk hydrothermal biochar is fully recyclable for multiple adsorption/desorption trials, which makes it extremely attractive for iodate contaminant separation.
Graphic abstract
The reliability function of variable-rate Slepian-Wolf coding is linked to the reliability function of channel coding with constant composition codes, through which computable lower and upper bounds ...are derived. The bounds coincide at rates close to the Slepian-Wolf limit, yielding a complete characterization of the reliability function in that rate region. It is shown that variable-rate Slepian-Wolf codes can significantly outperform fixed-rate Slepian-Wolf codes in terms of rate-error tradeoff. Variable-rate Slepian-Wolf coding with rate below the Slepian-Wolf limit is also analyzed. In sharp contrast with fixed-rate Slepian-Wolf codes for which the correct decoding probability decays to zero exponentially fast if the rate is below the Slepian-Wolf limit, the correct decoding probability of variable-rate Slepian-Wolf codes can be bounded away from zero.
We consider Slepian-Wolf code design based on low density parity-check (LDPC) coset codes. The density evolution formula for Slepian-Wolf coding is derived. An intimate connection between ...Slepian-Wolf coding and channel coding is then established. Specifically we show that, under density evolution, each Slepian-Wolf coding problem is equivalent to a channel coding problem for a binary-input output-symmetric channel.
A source coding paradigm called interactive encoding and decoding (IED) is considered for a source network where a finite alphabet source X is to be encoded, and another finite alphabet source Y ...correlated with X is available only to the decoder as a helper. The optimal performance achievable asymptotically (OPAA) by IED is investigated, where the performance is measured as the average number of bits per symbol exchanged by the encoder and decoder until the decoder learns X with high probability. First, it is shown that for any stationary (X , Y ), the OPAA by IED is given by the conditional entropy rate H ( X | Y ) of X given Y . This is in contrast with noninteractive Slepian-Wolf (SW) coding, where the OPAA is shown in general to be strictly greater than H ( X | Y ) when (X , Y ) is not ergodic. Second, for a memoryless source pair ( X, Y ), it is shown that IED approaches H ( X | Y ) faster than SW coding does. Finally, it is demonstrated that one can convert any classical universal data compression algorithm with side information to a universal IED algorithm for the class ¿ of all stationary ergodic source pairs. In contrast, universal SW coding algorithms for the class ¿ do not exist.
Causal video coding is a coding paradigm where video source frames X 1 , X 2 ,..., X N are encoded in a frame-by-frame manner, the encoder for each frame can use all previous source frames and all ...previous encoded frames, and the corresponding decoder can use only all previous encoded frames. In the special case where the encoder for each frame X k is further restricted to enlist help only from all previous encoded frames, causal video coding is reduced to predictive video coding, which all MPEG-series and H-series video coding standards proposed so far are based upon. In this paper, we compare the rate distortion performance of causal video coding with that of predictive video coding from an information theoretic perspective by modeling each frame X k itself as a source X k ={X k (i)} i=1 ∞ . Let R c *(D 1, ...,D N ) (R p *(D1,...,DN), respectively) denote the minimum total rate required to achieve a given distortion level D 1 ,...,D N in causal video coding (predictive video coding, respectively). We first show that like R c *(D1,..., D N ), for jointly stationary and totally ergodic sources X 1 , X 2 ,..., XN, R p *(D 1 ,...,D N ) is equal to the infimum of the nth order total rate distortion function R p,n (D1,...,DN) over all n, where R p,n (D 1 ,...,D N ) itself is given by the minimum of an information quantity over a set of auxiliary random variables. We then prove that if the jointly stationary and totally ergodic sources X 1 ,..., X N form a (first-order) Markov chain, we have R p *(D 1 ,...,D N )=R c *(D 1 ,...,D N ). However, this is not true in general if X 1 ,..., X N do not form a (first-order) Markov chain. Specifically, we demonstrate that for independent and identically distributed vector source (X 1 ,..., X N ), if X 1 ,..., X N do not form a (first-order) Markov chain, then under some conditions on source frames and distortion, R c *(D 1 ,..., D N ) is strictly less than R p *(D 1 ,..., D N ) in general. Our techniques allow us to compare R p *(D 1 ,..., D N ) with R c *(D 1 ,..., D N ) even when the single-letter characterization of R p *(D 1 ,..., D N ), if any, is unknown.
Causal video coding is considered from an information theoretic point of view, where video source frames X 1 , X 2 , ..., X N are encoded in a frame by frame manner, the encoder for each frame X k ...can use all previous frames and all previous encoded frames while the corresponding decoder can use only all previous encoded frames, and each frame X k itself is modeled as a source X k = {X k (i) } i=1 ∞ . A novel computation approach is proposed to analytically characterize, numerically compute, and compare the minimum total rate of causal video coding R c *(D 1 , ...,D N ) required to achieve a given distortion (quality) level D 1 , ...,D N >; 0. Among many other things, the computation approach includes an iterative algorithm with global convergence for computing R c *(D 1 , ...,D N ) . The global convergence of the algorithm further enables us to demonstrate a somewhat surprising result (dubbed the more and less coding theorem)-under some conditions on source frames and distortion, the more frames need to be encoded and transmitted, the less amount of data after encoding has to be actually sent. With the help of the algorithm, it is also shown by example that R c *(D 1 , ...,D N ) is in general much smaller than the total rate offered by the traditional greedy coding method. As a by-product, an extended Markov lemma is established for correlated ergodic sources.
On the Redundancy of Slepian-Wolf Coding Da-ke He; Lastras-Montano, L.A.; En-hui Yang ...
IEEE transactions on information theory,
12/2009, Letnik:
55, Številka:
12
Journal Article
Recenzirano
In this paper, the redundancy of both variable and fixed rate Slepian-Wolf coding is considered. Given any jointly memoryless source-side information pair {(Xi, Yi)} i=1 infin with finite alphabet, ...the redundancy R n (isin n ) of variable rate Slepian-Wolf coding of X 1 n with decoder only side information Y 1 n depends on both the block length n and the decoding block error probability isin n , and is defined as the difference between the minimum average compression rate of order n variable rate Slepian-Wolf codes having the decoding block error probability less than or equal to isin n , and the conditional entropy H(X|Y), where H(X|Y) is the conditional entropy rate of the source given the side information. The redundancy of fixed rate Slepian-Wolf coding of X 1 n with decoder only side information Y 1 n is defined similarly and denoted by R F n (isin n ). It is proved that under mild assumptions about isin n , R n (isin n ) = d v radic-log isin n /n + (oradic-log isin n /n) and R F n (isin n ) - d f radic-log isin n /n + o(radic-log isin n /n), where df and dnu are two constants completely determined by the joint distribution of the source-side information pair. Since d v is generally smaller than d f , our results show that variable rate Slepian-Wolf coding is indeed more efficient than fixed rate Slepian-Wolf coding.
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