arXiv subjects
Publications and source records attributed to Himanshu Asnani.
We consider the k-encoder source coding problem with a quadratic distortion measure. We show that among all source distributions with a given covariance matrix K, the jointly Gaussian source requires the highest rates in order to meet a given set of distortion constraints.
The problem of optimal actuation for channel and source coding was recently formulated and solved in a number of relevant scenarios. In this class of models, actions are taken at encoders or decoders, either to acquire side information in an efficient way or to control or probe effectively the channel state. In this paper, the problem of embedding information on the actions is studied for both the source and the channel coding set-ups. In both cases, a decoder is present that observes only a function of the actions taken by an encoder or a decoder of an action-dependent point-to-point link. For the source coding model, this decoder wishes to reconstruct a lossy version of the source being transmitted over the point-to-point link, while for the channel coding problem the decoder wishes to retrieve a portion of the message conveyed over the link. For the problem of source coding with actions taken at the decoder, a single letter characterization of the set of all achievable tuples of rate, distortions at the two decoders and action cost is derived, under the assumption that the mentioned decoder observes a function of the actions non-causally, strictly causally or causally. A special case of the problem in which the actions are taken by the encoder is also solved. A single-letter characterization of the achievable capacity-cost region is then obtained for the channel coding set-up with actions. Examples are provided that shed light into the effect of information embedding on the actions for the action-dependent source and channel coding problems.
Motivation: Next Generation Sequencing technologies revolutionized many fields in biology by enabling the fast and cheap sequencing of large amounts of genomic data. The ever increasing sequencing capacities enabled by current sequencing machines hold a lot of promise as for the future applications of these technologies, but also create increasing computational challenges related to the analysis and storage of these data. A typical sequencing data file may occupy tens or even hundreds of gigabytes of disk space, prohibitively large for many users. Raw sequencing data consists of both the DNA sequences (reads) and per-base quality values that indicate the level of confidence in the readout of these sequences. Quality values account for about half of the required disk space in the commonly used FASTQ format and therefore their compression can significantly reduce storage requirements and speed up analysis and transmission of these data. Results: In this paper we present a framework for the lossy compression of the quality value sequences of genomic read files. Numerical experiments with reference based alignment using these quality values suggest that we can achieve significant compression with little compromise in performance for several downstream applications of interest, as is consistent with our theoretical analysis. Our framework also allows compression in a regime - below one bit per quality value - for which there are no existing compressors.
We study cooperation in multi terminal source coding models involving successive refinement. Specifically, we study the case of a single encoder and two decoders, where the encoder provides a common description to both the decoders and a private description to only one of the decoders. The decoders cooperate via cribbing, i.e., the decoder with access only to the common description is allowed to observe, in addition, a deterministic function of the reconstruction symbols produced by the other. We characterize the fundamental performance limits in the respective settings of non-causal, strictly-causal and causal cribbing. We use a new coding scheme, referred to as Forward Encoding and Block Markov Decoding, which is a variant of one recently used by Cuff and Zhao for coordination via implicit communication. Finally, we use the insight gained to introduce and solve some dual channel coding scenarios involving Multiple Access Channels with cribbing.
We consider multi-terminal source coding with a single encoder and multiple decoders where either the encoder or the decoders can take cost constrained actions which affect the quality of the side information present at the decoders. For the scenario where decoders take actions, we characterize the rate-cost trade-off region for lossless source coding, and give an achievability scheme for lossy source coding for two decoders which is optimum for a variety of special cases of interest. For the case where the encoder takes actions, we characterize the rate-cost trade-off for a class of lossless source coding scenarios with multiple decoders. Finally, we also consider extensions to other multi-terminal source coding settings with actions, and characterize the rate -distortion-cost tradeoff for a case of successive refinement with actions.
A real time coding system with lookahead consists of a memoryless source, a memoryless channel, an encoder, which encodes the source symbols sequentially with knowledge of future source symbols upto a fixed finite lookahead, d, with or without feedback of the past channel output symbols and a decoder, which sequentially constructs the source symbols using the channel output. The objective is to minimize the expected per-symbol distortion. For a fixed finite lookahead d>=1 we invoke the theory of controlled markov chains to obtain an average cost optimality equation (ACOE), the solution of which, denoted by D(d), is the minimum expected per-symbol distortion. With increasing d, D(d) bridges the gap between causal encoding, d=0, where symbol by symbol encoding-decoding is optimal and the infinite lookahead case, d=\infty, where Shannon Theoretic arguments show that separation is optimal. We extend the analysis to a system with finite state decoders, with or without noise-free feedback. For a Bernoulli source and binary symmetric channel, under hamming loss, we compute the optimal distortion for various source and channel parameters, and thus obtain computable bounds on D(d). We also identify regions of source and channel parameters where symbol by symbol encoding-decoding is suboptimal. Finally, we demonstrate the wide applicability of our approach by applying it in additional coding scenarios, such as the case where the sequential decoder can take cost constrained actions affecting the quality or availability of side information about the source.
In this paper we consider a multiple access channel (MAC) with partial cribbing encoders. This means that each of two encoders obtains a deterministic function of the other encoder output with or without delay. The partial cribbing scheme is especially motivated by the additive noise Gaussian MAC since perfect cribbing results in the degenerated case of full cooperation between the encoders and requires an infinite entropy link. We derive a single letter characterization of the capacity of the MAC with partial cribbing for the cases of causal and strictly causal partial cribbing. Several numerical examples, such as quantized cribbing, are presented. We further consider and derive the capacity region where the cribbing depends on actions that are functions of the previous cribbed observations. In particular, we consider a scenario where the action is "to crib or not to crib" and show that a naive time-sharing strategy is not optimal.
We consider the problem of optimal probing of states of a channel by transmitter and receiver for maximizing rate of reliable communication. The channel is discrete memoryless (DMC) with i.i.d. states. The encoder takes probing actions dependent on the message. It then uses the state information obtained from probing causally or non-causally to generate channel input symbols. The decoder may also take channel probing actions as a function of the observed channel output and use the channel state information thus acquired, along with the channel output, to estimate the message. We refer to the maximum achievable rate for reliable communication for such systems as the 'Probing Capacity'. We characterize this capacity when the encoder and decoder actions are cost constrained. To motivate the problem, we begin by characterizing the trade-off between the capacity and fraction of channel states the encoder is allowed to observe, while the decoder is aware of channel states. In this setting of 'to observe or not to observe' state at the encoder, we compute certain numerical examples and note a pleasing phenomenon, where encoder can observe a relatively small fraction of states and yet communicate at maximum rate, i.e. rate when observing states at encoder is not cost constrained.
We consider the effects of Rayleigh fading and lognormal shadowing in the physical interference model for all the successful transmissions of traffic across the network. New bounds are derived for the capacity of a given random ad hoc wireless network that reflect packet drop or capture probability of the transmission links. These bounds are based on a simplified network topology termed as honey-comb topology under a given routing and scheduling scheme.