Z-channel

About: Z-channel is a research topic. Over the lifetime, 82 publications have been published within this topic receiving 4183 citations.

A new achievable rate region for the interference channel

Abstract: A new achievable rate region for the general interference channel which extends previous results is presented and evaluated. The technique used is a generalization of superposition coding to the multivariable case. A detailed computation for the Gaussian channel case clarifies to what extent the new region improves previous ones. The capacity of a class of Gaussian interference channels is also established.

Gaussian Interference Channel Capacity to Within One Bit

Abstract: The capacity of the two-user Gaussian interference channel has been open for 30 years. The understanding on this problem has been limited. The best known achievable region is due to Han and Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a very simple and explicit Han-Kobayashi type scheme can achieve to within a single bit per second per hertz (bit/s/Hz) of the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high signal-to-noise ratio (SNR) regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

Channel dispersion and moderate deviations limits for memoryless channels

Abstract: Recently, Altug and Wagner [1] posed a question regarding the optimal behavior of the probability of error when channel coding rate converges to the capacity sufficiently slowly. They gave a sufficient condition for the discrete memoryless channel (DMC) to satisfy a moderate deviation property (MDP) with the constant equal to the channel dispersion. Their sufficient condition excludes some practically interesting channels, such as the binary erasure channel and the Z-channel. We extend their result in two directions. First, we show that a DMC satisfies MDP if and only if its channel dispersion is nonzero. Second, we prove that the AWGN channel also satisfies MDP with a constant equal to the channel dispersion. While the methods used by Altug and Wagner are based on the method of types and other DMC-specific ideas, our proofs (in both achievability and converse parts) rely on the tools from our recent work [2] on finite-blocklength regime that are equally applicable to non-discrete channels and channels with memory.

Adaptive message routing for multi-dimensional networks

Abstract: An adaptive routing means and method useful for transferring messages on a number of multi-dimensional network topologies that connect distributed multi-processing systems. A plurality of processing nodes comprising processing means for processing information and router means for routing messages are connected in a multi-dimensional network (A) with an identical or redundant message passing multi-dimensional network (B) of routers being connected to network A. Each router comprises four types of channels for message passing: 1) a channel to transfer information between a router and a processor coupled to the router, 2) a channel to transfer information in an X direction, 3) a channel for the Y direction, and 4) a channel for the Z direction. This connectivity allows messages to pass between nodes within network A, between routers within network B, or between network A and network B by passing through a router. Messages are routed in networks A and B by routing first in the X dimension and then in the Y dimension. The present invention transitions between A and B networks when contention is encountered in the X or Y direction, if the appropriate Z channel is available. If an X or Y channel is not immediately granted, a request is made for the Z channel. Both the request for an X or Y channel and the request for the Z channel are maintained until one request is granted. The message is then routed on the granted channel and the other request is withdrawn. The router does not commit to routing on a particular channel until one channel is available.

The uniform distribution as a universal prior

Abstract: In this correspondence, we discuss the properties of the uniform prior as a universal prior, i.e., a prior that induces a mutual information that is simultaneously close to the capacity for all channels. We determine bounds on the amount of the mutual information loss in using the uniform prior instead of the capacity-achieving prior. Specifically, for the class of binary input channels with any output alphabet, we show that the Z-channel has the minimal mutual information with uniform prior, out of all channels with a given capacity. From this, we conclude that the degradation of the mutual information with respect to the capacity is at most 0.011 bit, and as was shown previously, at most 6%. A related result is that the capacity-achieving prior, for any channel, is not far from uniform. Some of these results are extended to channels with nonbinary input.