Noise prediction for channels with side information at the transmitter

Costa's celebrated "writing on dirty paper" (WDP) shows that the powerconstrained channel Y = X + S + Z, with Gaussian Z, has the same capacity as the standard AWGN channel Y = X + Z, provided that the "interference" S (no matter how strong it is) is known at the transmitter. While this ability for perfect interference cancelation is very appealing, it relies heavily on the Gaussianity of the (unknown) noise Z. We construct an example of "bad" noise for writing on dirty paper, namely, "difference set noise". If the interference S is strong, then difference-set noise limits the WDP capacity to at most 2 bits. At the same time, like in the AWGN case, the zero-interference capacity grows without bound with the input constraint. Thus almost 100 % of the available capacity is lost in WDP in the presence of difference-set noise. This high capacity loss is due to the "entropy amplification property" (EAP) of noise with an aperiodic probability distribution. Using the EAP and the duality between WDP and Wyner-Ziv source coding, we also give an example of dramatic rate-loss in quantizing encrypted source.

mentioning

confidence: 99%

Entropy Amplification Property and the Loss for Writing on Dirty Paper

Cohen

Zamir

2008

“…We rely on the analysis of Erez and Zamir in [17]. They considered Shannon's model [27] of a channel with random parameters with causal SI, where the state sequence S n is i.i.d.…”

Section: A6 Analysis Of Examplementioning

confidence: 99%

“…according to a given distribution q(s). In [17], Erez and Zamir consider a modulo-additive channel, {0, 1, . . .…”

Section: A6 Analysis Of Examplementioning

confidence: 99%

The Arbitrarily Varying Broadcast Channel With Causal Side Information at the Encoder

Pereg

Steinberg

2020

In this work, we study two models of arbitrarily varying channels, when causal side information is available at the encoder in a causal manner. First, we study the arbitrarily varying channel (AVC) with input and state constraints, when the encoder has state information in a causal manner. Lower and upper bounds on the random code capacity are developed. A lower bound on the deterministic code capacity is established in the case of a message-averaged input constraint. In the setting where a state constraint is imposed on the jammer, while the user is under no constraints, the random code bounds coincide, and the random code capacity is determined. Furthermore, for this scenario, a generalized non-symmetrizability condition is stated, under which the deterministic code capacity coincides with the random code capacity.A second model considered in our work is the arbitrarily varying degraded broadcast channel with causal side information at the encoder (without constraints). We establish inner and outer bounds on both the random code capacity region and the deterministic code capacity region. The capacity region is then determined for a class of channels satisfying a condition on the mutual informations between the strategy variables and the channel outputs. As an example, we show that the condition holds for the arbitrarily varying binary symmetric broadcast channel, and we find the corresponding capacity region. 4 1.1 Definitions and Previous Results

“…In particular, the definition of cyclic shift symmetry extends naturally for : If is invariant under any modular shift in the input PDF, the channel is cyclic shift symmetric. Typical examples of continuous alphabet cyclic shift symmetric channels are modulo additive noise channels [14]. If cyclic shift symmetry holds, the channel capacity is achieved at uniform distribution over .…”

Section: Corollarymentioning

confidence: 99%

Wiretap Channels: Implications of the More Capable Condition and Cyclic Shift Symmetry

Özel

Ulukuş

2013

Abstract-Characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables:, for rate splitting and , for channel prefixing. In this paper, we explore specific classes of wiretap channels for which the evaluation of the rate-equivocation region is simpler. We show that if the wiretap channel is more capable, is optimal and the boundary of the rate-equivocation region is achieved by varying rate splitting alone. Conversely, we show under a mild condition that if the wiretap channel is not more capable, then is strictly suboptimal. Next, we focus on the class of cyclic shift symmetric wiretap channels. We show that optimal rate splitting that achieves the boundary of the rate-equivocation region is uniform with cardinality and the prefix channel between optimal and is expressed as cyclic shifts of the solution of an auxiliary optimization problem over a single variable. We provide a special class of cyclic shift symmetric wiretap channels for which is optimal. We apply our results to the binary-input cyclic shift symmetric wiretap channels and thoroughly characterize the rate-equivocation regions of the BSC-BEC and BEC-BSC wiretap channels.