Himanshu Asnani

Scheduling with limited information in wireless systems

Opportunistic scheduling is a key mechanism for improving the performance of wireless systems. However, this mechanism requires that transmitters are aware of channel conditions (or CSI, Channel State Information) to the various possible receivers. CSI is not automatically available at the transmitters, rather it has to be acquired. Acquiring CSI consumes resources, and only the remaining resources can be used for actual data transmissions. We explore the resulting trade-off between acquiring CSI and exploiting channel diversity to the various receivers. Specifically, we consider a system consisting of a transmitter and a fixed number of receivers/users. An infinite buffer is associated to each receiver, and packets arrive in this buffer according to some stochastic process with fixed intensity. We study the impact of limited channel information on the stability of the system. We characterize its stability region, and show that an adaptive queue length-based policy can achieve stability whenever doing so is possible. We formulate a Markov Decision Process problem to characterize this queue length-based policy. In certain specific and yet relevant cases, we explicitly compute the optimal policy. In general case, we provide a scheduling policy that achieves a fixed fraction of the systems stability region. Scheduling with limited information is a problem that naturally arises in cognitive radio systems, and our results can be used in these systems.

QualComp: a new lossy compressor for quality scores based on rate distortion theory.

BackgroundNext Generation Sequencing technologies have revolutionized many fields in biology by reducing the time and cost required for sequencing. As a result, large amounts of sequencing data are being generated. A typical sequencing data file may occupy tens or even hundreds of gigabytes of disk space, prohibitively large for many users. This data consists of both the nucleotide sequences and per-base quality scores that indicate the level of confidence in the readout of these sequences. Quality scores account for about half of the required disk space in the commonly used FASTQ format (before compression), and therefore the compression of the quality scores can significantly reduce storage requirements and speed up analysis and transmission of sequencing data.ResultsIn this paper, we present a new scheme for the lossy compression of the quality scores, to address the problem of storage. Our framework allows the user to specify the rate (bits per quality score) prior to compression, independent of the data to be compressed. Our algorithm can work at any rate, unlike other lossy compression algorithms. We envisage our algorithm as being part of a more general compression scheme that works with the entire FASTQ file. Numerical experiments show that we can achieve a better mean squared error (MSE) for small rates (bits per quality score) than other lossy compression schemes. For the organism PhiX, whose assembled genome is known and assumed to be correct, we show that it is possible to achieve a significant reduction in size with little compromise in performance on downstream applications (e.g., alignment).ConclusionsQualComp is an open source software package, written in C and freely available for download at https://sourceforge.net/projects/qualcomp.

Learning to Optimally Exploit Multi-Channel Diversity in Wireless Systems

Consider a wireless system where a transmitter may send data to a set of receivers, or on various channels, experiencing random time-varying fading. The transmitter can send data to a single receiver or on a single channel at a time and may adapt its transmission power to the radio conditions of the chosen receiver/channel. Its objective is to implement a strategy defining at each time how to select the receiver/channel and transmission power, so as to maximize its throughput, i.e., its average sending rate, under an average power constraint. The optimization problem is easy when the fading conditions of all the receivers/channels are known. In many situations however, the instantaneous fading conditions are not known a priori, instead they have to be acquired, i.e., receivers/channels have to be probed, which consumes resources (time, spectrum, energy) in proportion of the number of probed receivers/channels. Hence, the transmitter may choose not to acquire the radio conditions of all the receivers/channels so as to spare resources for actual transmissions. In this paper, we aim at characterizing a joint probing, receiver/channel selection and power control strategy maximizing throughput. We provide an adaptive algorithm converging to the throughput optimal strategy. This algorithm may be used in a wide class of wireless systems with limited information, such as broadcast systems without a priori knowledge of the instantaneous Channel-State Information (CSI). But it can be also used to solve dynamic spectrum access problems such as those arising in cognitive radio systems, where secondary users can access large parts of the spectrum, but have to discover which portions of the spectrum offer more favorable radio conditions or less interference from primary users.

Real-Time Coding With Limited Lookahead

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 = ∞, where Shannon Theoretic arguments show that separation is optimal. We extend the analysis to a system with finite state decoders. 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 sub-optimal. 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.

Multiple-Access Channel With Partial and Controlled Cribbing Encoders

In this paper, we consider a multiple-access channel (MAC) with partial cribbing encoders. This means that each of the two encoders obtains a deterministic function of the output of the other encoder with or without delay. The partial cribbing scheme is especially motivated by the additive noise Gaussian MAC, where 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 cribbing. Several numerical examples, such as those of 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 taken to decide “to crib or not to crib” and show that a naive time-sharing strategy is not optimal.

Capacity of a POST Channel With and Without Feedback

We consider finite state channels, where the state of the channel is its previous output. We refer to these as Previous Output is the STate (POST) channels. We first focus on POST(α) channels. These channels have binary inputs and outputs, where the state determines if the channel behaves as a Z or an S channel, both with parameter α. We show that the nonfeedback capacity of the POST(α) channel equals its feedback capacity, despite the memory of the channel. The proof of this surprising result is based on showing that the induced output distribution, when maximizing the directed information in the presence of feedback, can also be achieved by an input distribution that does not utilize the feedback. We show that this is a sufficient condition for the feedback capacity to equal the nonfeedback capacity for any finite state channel. We show that the result carries over from the POST(α) channel to a binary POST channel, where the previous output determines whether the current channel will be binary with parameters (a, b) or (b, a). Finally, we show that, in general, feedback may increase the capacity of a POST channel.

Multi-terminal source coding with action dependent side information

We consider multi-terminal source coding with a single encoder and multiple decoders where either the encoder or the decoders can take actions which affect the quality or availability of the side information present at the decoders, subjected to an additional cost constraint on the actions taken. For the scenario where a joint action is taken at the decoders, 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 several special cases. 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.

Successive Refinement With Decoder Cooperation and Its Channel Coding Duals

We study cooperation in multiterminal 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 noncausal, strictly causal, and causal cribbing. We use a coding scheme, referred to as Forward Encoding and Block Markov Decoding, which builds on 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.

To Feed or Not to Feedback

We study communication over finite state channels (FSCs), where the encoder and the decoder can control the availability or the quality of noise-free feedback, which is fed back from the decoder to the encoder. Specifically, the instantaneous feedback is a function of an action taken by the encoder, an action taken by the decoder, and the channel output. Encoder and decoder actions take values from finite alphabet sets and may be subject to average cost constraints. We prove capacity results for such a setting by constructing a sequence of codes, using a simple scheme based on code tree, which generates channel input symbols along with encoder and decoder actions. We prove that the limit of this sequence exists, and provide an upper bound on the maximum achievable rate. Our upper and lower bounds coincide and hence yield the capacity for the case where the probability of initial state is positive for all states. Next, the capacity is given for indecomposable channels without intersymbol interference as the limit of normalized directed information between the input and output sequences, maximized over an appropriate set of causally conditioned distributions. As a special case of our framework, we characterize the capacity of coding on the backward link in FSCs, i.e., when the decoder sends limited-rate instantaneous coded noise-free feedback on the backward link. Finally, we propose an extension of the Blahut-Arimoto algorithm for evaluating the capacity when actions can be cost constrained and demonstrate its application in a few examples. Among these examples are those of to feed or not to feedback where the encoder takes binary actions that determine whether the current channel output will be fed back to the encoder, with a constraint on the fraction of channel outputs that are fed back.

On real time coding with limited lookahead

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 up to 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=∞, 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.