Farhad Shirani

Finite block-length gains in distributed source coding

A new coding scheme for the distributed source coding problem for general discrete memoryless sources is presented. The scheme involves a two-layered coding strategy, the first layer code is of constant finite block-length whereas the second layer contains codes of block-length approaching infinity. It is argued that small block-length codes preserve correlations between sources more efficiently, while suffering rate-loss in a point-to-point compression perspective. Consequently, there is a sweet-spot for the length of the code. An achievable rate-distortion region is characterized using single-letter distributions. It is shown that this region strictly contains previous known achievable rate-distortion regions for the distributed source coding problem.

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 for discrete memoryless sources. 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.

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

We consider the problem of multiple descriptions (MDs) 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

On the necessity of structured codes for communications over MAC with feedback

l

New sufficient conditions for Multiple-Access Channel with correlated sources

-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 the specific MD examples involving three or more descriptions. We show that the application of structured quantizers results in strict RD improvements when there are more than two descriptions. Furthermore, we show that a 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 RD region using computable single-letter information quantities. The new RD region strictly contains all of the previous known achievable regions.

Quasi Linear Codes: Application to point-to-point and multi-terminal source coding

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 [1]; 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.

Beyond group capacity in multi-terminal communications

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 argue that if the sources impose certain algebraic structures, then the application of structured codes improves upon the CES scheme. Based on this notion, we use a combination of the CES 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 a three-user MAC with binary inputs. Using this example, we show strict improvements over the CES scheme.

New lattice codes for multiple-descriptions

A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLCs are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under addition. We argue that these codes provide gains in terms of achievable Rate-Distortions (RD) in different multi-terminal source coding problems. We derive the necessary covering bounds for analyzing the performance of QLCs. We then consider the Multiple-Descriptions (MD) problem, and prove through an example that the application of QLCs gives an improved achievable RD region for this problem. Finally, we derive an inner bound to the achievable RD region for the general MD problem which strictly contains all of the previous known achievable regions.

Trade-off between communication and cooperation in the Interference Channel

A new structured coding scheme based on transversal group codes is proposed. We investigate the information theoretic performance limits for this strategy in multi-terminal communications. Achievability results are derived for lossless reconstruction of sum of two sources. In addition, a new rate region is presented for the problem of computation over multiple access channel. We show that the application of the new coding strategy, results in strict gains in terms of achievable rates in both settings.

An information theoretic framework for active de-anonymization in social networks based on group memberships

A new coding scheme for the L-descriptions problem is proposed. In particular we consider continuous sources and lattice quantizers. New covering and packing bounds for using nested lattices are derived. We prove through an example that using nested lattice quantizers instead of independently generated codebooks results in gains.