arXiv subjects

Farhad Shirani

Publications and source records attributed to Farhad Shirani.

45 records · Page 3Linked to original sources

arXiv2017

How to Compute Modulo Prime-Power Sums ?

A new class of structured codes called Quasi Group Codes (QGC) is introduced. A QGC is a subset of a group code. In contrast with group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen such that the size of $\mathcal{C}+\mathcal{C}$ is equal to any number between $|\mathcal{C}|$ and $|\mathcal{C}|^2$ . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typical set corresponding to these single-letter distributions. The asymptotic performance limits of this class of QGCs is characterized using single-letter information quantities. Corresponding covering and packing bounds are derived. It is shown that the point-to-point channel capacity and optimal rate-distortion function are achievable using QGCs. Coding strategies based on QGCs are introduced for three fundamental multi-terminal problems: the Körner-Marton problem for modulo prime-power sums, computation over the multiple access channel (MAC), and MAC with distributed states. For each problem a single-letter achievable rate-region is derived. It is shown, through examples, that the coding strategies improve upon the previous strategies based on unstructured codes, linear codes and group codes.

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arXiv2017

On the Sub-optimality of Single-Letter Coding over Networks

In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a new upper bound on the correlation between the outputs of these functions. The upper bound may find applications in problems in many areas which deal with common information. We build upon Witsenhausen's result on maximum correlation. The present upper bound takes into account the effective length of the Boolean functions in characterizing the correlation. We use the new bound to characterize the communication-cooperation tradeoff in multi-terminal communications. We investigate binary block-codes (BBC). A BBC is defined as a vector of Boolean functions. We consider an ensemble of BBCs which is randomly generated using single-letter distributions. We characterize the vector of dependency spectrums of these BBCs. We use this vector to bound the correlation between the outputs of two distributed BBCs. Finally, the upper bound is used to show that the large blocklength single-letter coding schemes studied in the literature are sub-optimal in various multi-terminal communication settings.

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arXiv2017

On the Necessity of Structured Codes for Communications over MAC with Feedback

The problem of three-user multiple-access channel (MAC) with noiseless feedback is investigated. A new coding strategy is presented. The coding scheme builds upon the natural extension of the Cover-Leung (CL) scheme; and uses quasi-linear codes. A new single-letter achievable rate region is derived. The new achievable region strictly contains the CL region. This is shown through an example. In this example, the coding scheme achieves optimality in terms of transmission rates. It is shown that any optimality achieving scheme for this example must have a specific algebraic structure. Particularly, the codebooks must be closed under binary addition.

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arXiv2017

A New Achievable Rate Region for Multiple-Access Channel with States

The problem of reliable communication over the multiple-access channel (MAC) with states is investigated. We propose a new coding scheme for this problem which uses quasi-group codes (QGC). We derive a new computable single-letter characterization of the achievable rate region. As an example, we investigate the problem of doubly-dirty MAC with modulo-$4$ addition. It is shown that the sum-rate $R_1+R_2=1$ bits per channel use is achievable using the new scheme. Whereas, the natural extension of the Gel'fand-Pinsker scheme, sum-rates greater than $0.32$ are not achievable.

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arXiv2017

On the Sub-optimality of Single-letter Coding in Multi-terminal Communications

We investigate binary block-codes (BBC). A BBC is defined as a vector of Boolean functions. We consider BBCs which are generated randomly, and using single-letter distributions. We characterize the vector of dependency spectrums of these BBCs. We use this vector to upper-bound the correlation between the outputs of two distributed BBCs. Finally, the upper-bound is used to show that the large blocklength single-letter coding schemes in the literature are sub-optimal in some multiterminal communication settings.

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arXiv2017

On the Correlation between Boolean Functions of Sequences of Random Variables

In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a new upper-bound on the correlation between the outputs of these functions. The upper-bound is useful in various disciplines which deal with common-information. We build upon Witsenhausen's bound on maximum-correlation. The previous upper-bound did not take the effective length of the Boolean functions into account.

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arXiv2016

New Sufficient Conditions for Multiple-Access Channel with Correlated Sources

The problem of three-user Multiple-Access Channel (MAC) with correlated sources is investigated. An extension to the Cover-El Gamal-Salehi (CES) scheme is introduced. We use a combination of this scheme with linear codes and propose a new coding strategy. We derive new sufficient conditions to transmit correlated sources reliably. We consider an example of three-user MAC with binary inputs. Using this example, we show strict improvements over the CES scheme.

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arXiv2016

An Achievable Rate-Distortion Region for Multiple Descriptions Source Coding Based on Coset Codes

We consider the problem of multiple descriptions (MD) source coding and propose new coding strategies involving both unstructured and structured coding layers. Previously, the most general achievable rate-distortion (RD) region for the $l$-descriptions problem was the Combinatorial Message Sharing with Binning (CMSB) region. The CMSB scheme utilizes unstructured quantizers and unstructured binning. In the first part of the paper, we show that this strategy can be improved upon using more general unstructured quantizers and a more general unstructured binning method. In the second part, structured coding strategies are considered. First, structured coding strategies are developed by considering specific MD examples involving three or more descriptions. We show that application of structured quantizers results in strict RD improvements when there are more than two descriptions. Furthermore, we show that structured binning also yields improvements. These improvements are in addition to the ones derived in the first part of the paper. This suggests that structured coding is essential when coding over more than two descriptions. Using the ideas developed through these examples we provide a new unified coding strategy by considering several structured coding layers. Finally, we characterize its performance in the form of an inner bound to the optimal rate-distortion region using computable single-letter information quantities. The new RD region strictly contains all of the previous known achievable regions.

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arXiv2014

An Achievable Rate-Distortion Region for the Multiple Descriptions Problem

A multiple-descriptions (MD) coding strategy is proposed and an inner bound to the achievable rate-distortion region is derived. The scheme utilizes linear codes. It is shown in two different MD set-ups that the linear coding scheme achieves a larger rate-distortion region than previously known random coding strategies. Furthermore, it is shown via an example that the best known random coding scheme for the set-up can be improved by including additional randomly generated codebooks.

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