Uncoded Side Information Research Articles

A Novel & Stable Stochastic-Mean-Field-Game for Lossy Source-Coding Paradigms: A Many-Body-Theoretic Perspective

Adaptive controllers and signal processors play a key role in dealing with parameter uncertainties. This paper proposes an adaptive and new information theoretic algorithm for secure and optimal source-coding. We optimise the volume of the achievable rate-distortion-equivocation region by the private Helen’s rate (HR), defining a stochastic mean-field game (MFG). The aforementioned stochasticity deals with the additional uncoded side-information (SI) at the encoder-decoder, or even possibly-decoded SI at the eavesdropper (Eve). The stochastic partial derivative equations (SPDEs), namely the Hamilton-Jacobi-Bellman (HJB) and the Fokker-Planck-Kolmogorov (FPK) are presented, being solved by a discretised Lagrangian. We explore the Information-flow over the resultant Riemann-Sphere and our proposed SMFG’s stability from a many-body-theoretic perspective. We also show that while the equivocation (uncertainty) rate is $\Delta \le min \{\mathcal {H}(\mathcal {X}),\mathcal {R}_{h} \}$ , $\mathcal {I}(\mathcal {Y};\mathcal {Z}|\mathcal {W})$ which is upper-bounded to $min\{ \mathcal {I}(\mathcal {X};\mathcal {Y}),\mathcal {I}(\mathcal {Y};\mathcal {Z}|\mathcal {W}) \}$ , versus $\mathcal {I}(\mathcal {X};\mathcal {Z}|\mathcal {W})$ theoretically converges to the information-Bottleneck-bound $\mathcal {H}(\mathcal {X})$ . Simulation results also show an out-performance of our scheme over the existing work, proving the SMFG’s stability and an adequate distance to Pareto-Optimal sets . Our generic solution covers a comprehensive field of studies determining smooth non-linearity .

Secure Multiterminal Source Coding With Side Information at the Eavesdropper

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate—average uncertainty—at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger–Tung and the secure source coding setups. Inner and outer bounds on the so-called rate-distortion-equivocation region are derived. The inner region turns to be tight for two cases: 1) uncoded side information at Bob and 2) lossless reconstruction of both sources at Bob—secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (respectively) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a nonzero distortion at Bob can be fully exploited to guarantee secrecy.

Secure Source Coding With a Helper

We consider a secure lossless source coding problem with a rate-limited helper. In particular, Alice observes an independent and identically distributed (i.i.d.) source $X^{n}$ and wishes to transmit this source losslessly to Bob over a rate-limited link of capacity not exceeding $R_{x}$ . A helper, say Helen, observes an i.i.d. correlated source $Y^{n}$ and can transmit information to Bob over another link of capacity not exceeding $R_{y}$ . A passive eavesdropper (say Eve) can observe the coded output of Alice, i.e., the link from Alice to Bob is public. The uncertainty about the source $X^{n}$ at Eve (denoted by $\Delta$ ) is measured by the conditional entropy ${{H(X^{n}\vert J_{x})}\over{n}}$ , where $J_{x}$ is the coded output of Alice and $n$ is the block length. We completely characterize the rate-equivocation region for this secure source coding model, where we show that Slepian–Wolf binning of $X^{n}$ with respect to the coded side information received at Bob is optimal. We next consider a modification of this model in which Alice also has access to the coded output of Helen. We call this model as the two-sided helper model. For the two-sided helper model, we characterize the rate-equivocation region. While the availability of side information at Alice does not reduce the rate of transmission from Alice, it significantly enhances the resulting equivocation at Eve. In particular, the resulting equivocation for the two-sided helper case is shown to be $\min (H(X),R_{y})$ , i.e., one bit from the two-sided helper provides one bit of uncertainty at Eve. From this result, we infer that Slepian–Wolf binning of $X$ is suboptimal and one can further decrease the information leakage to the eavesdropper by utilizing the side information at Alice. We, finally, generalize both of these results to the case in which there is additional uncoded side information $W^{n}$ available at Bob and characterize the rate-equivocation regions under the assumption that $Y^{n}\rightarrow X^{n}\rightarrow W^{n}$ forms a Markov chain.

Precoding and Decoding Paradigms for Distributed Vector Data Compression

In this paper, we consider the problem of lossy coding of correlated vector sources with uncoded side information available at the decoder. In particular, we consider lossy coding of vector source xisinR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> which is correlated with vector source yisinR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> , known at the decoder. We propose two compression schemes, namely, distributed adaptive compression (DAC) and distributed universal compression (DUC) schemes. The DAC algorithm is inspired by the optimal solution for Gaussian sources and requires computation of the conditional Karhunen-Loegraveve transform (CKLT) of the data at the encoder. The DUC algorithm, however, does not require knowledge of the CKLT at the encoder. The DUC algorithms are based on the approximation of the correlation model between the sources y and x through a linear model y=Hx+n in which H is a matrix and n is a random vector and independent of x. This model can be viewed as a fictitious communication channel with input x and output y. Utilizing channel equalization at the receiver, we convert the original vector source coding problem into a set of manageable scalar source coding problems. Furthermore, inspired by bit loading strategies employed in wireless communication systems, we propose for both compression schemes a rate allocation policy which minimizes the decoding error rate under a total rate constraint. Equalization and bit loading are paired with a quantization scheme for each vector source entry (a slightly simplified version of the so called DISCUS scheme). The merits of our work are as follows: 1) it provides a simple, yet optimized, implementation of Wyner-Ziv quantizers for correlated vector sources, by using the insight gained in the design of communication systems; 2) it provides encoding schemes that, with or without the knowledge of the correlation model at the encoder, enjoy distributed compression gains

Capacity of channels with uncoded side information

AbstractParallel independent channels where no encoding is allowed for one of the channels are studied. The Slepian‐Wolf theorem on source coding of correlated sources is used to show that any information source whose entropy rate is below the sum of the capacity of the coded channel and the input/output mutual information of the uncoded channel is transmissible with arbitrary reliability. The converse is also shown. Thus, coding of the side information channel is unnecessary when its mutual information is maximized by the source distribution. Applications to superposed coded/uncoded transmission on Gaussian channels are studied and an information‐theoretic interpretation of Parallel‐Concatenated channel codes and, in particular. Turbo codes is put forth.