Aria Ghasemian Sahebi

Multilevel polarization of polar codes over arbitrary discrete memoryless channels

It is shown that the original construction of polar codes suffices to achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two, levels so that the synthesized channels are either useless, perfect or “partially perfect”. Given a coset decomposition of the input alphabet, there exists a corresponding partially perfect channel whose outputs uniquely determine the coset where the channel input symbol belongs to. By a slight modification of the encoding and decoding rules, it is shown that perfect transmission of certain information letters over partially perfect channels is possible. It is also shown through an example that polar codes do not achieve the capacity of coset codes over arbitrary channels.

Multilevel Channel Polarization for Arbitrary Discrete Memoryless Channels

It is shown that polar codes, with their original (u,u+v) kernel, achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two levels so that the synthesized channels are either useless, perfect or “partially perfect.” Any subset of the channel input alphabet which is closed under addition induces a coset partition of the alphabet through its shifts. For any such partition of the input alphabet, there exists a corresponding partially perfect channel whose outputs uniquely determine the coset to which the channel input belongs. By a slight modification of the encoding and decoding rules, it is shown that perfect transmission of certain information symbols over partially perfect channels is possible. Our result is general regarding both the cardinality and the algebraic structure of the channel input alphabet; i.e., we show that for any channel input alphabet size and any Abelian group structure on the alphabet, polar codes are optimal. Due to the modifications, we make to the encoding rule of polar codes, the constructed codes fall into a larger class of structured codes called nested group codes.

On distributed source coding using Abelian group codes

In this paper, we consider the distributed source coding problem with a joint distortion criterion. We use random structured codes, specifically nested Abelian group codes to achieve a new inner bound to the rate-distortion region. This new inner bound unifies all other known results on the distributed source coding problem and for certain sources, this inner bound is strictly larger than other known rate regions. Furthermore, we define the notion of “nested random/group codes” in which the inner code is a group code and the outer code is a random code such that the quantization operation is a random vector quantization and the binning operation is correlated. We use random/group codes to improve upon the rate region achieved using nested group codes. We define two fundamental quantities of Abelian group codes: the “channel coding group entropy” and the “source coding group entropy” to present the achievable rate region.

A new achievable rate region for the 3-user discrete memoryless interference channel

The 3-user discrete memoryless interference channel is considered in this paper. We provide a new inner bound (achievable rate region) to the capacity region for this channel. This inner bound is based on a new class of code ensembles based on asymptotically good nested linear codes. This achievable region is strictly superior to the straightforward extension of Han-Kobayashi rate region from the case of two-users to three-users. This rate region is characterized using single-letter information quantities. We consider examples to illustrate the rate region.

On the capacity of Abelian group codes over discrete memoryless channels

For most discrete memoryless channels, there does not exist a linear code which uses all of the channels input symbols. Therefore, linearity of the code for such channels is a very restrictive condition and there should be a loosening of the algebraic structure of the code to a degree that the code can admit any channel input alphabet. For any channel input alphabet size, there always exists an Abelian group structure defined on the alphabet. We investigate the capacity of Abelian group codes over discrete memoryless channels and provide lower and upper bounds on the capacity.

Distributed source coding in absence of common components

We introduce a scheme for the binary one-help-one distributed source coding problem using two layers of codes. The primary code is of constant finite block-length and the secondary code has a block-length approaching infinity. The achievable rate-distortion region for this scheme is derived for the binary one-help-one problem. It is shown that the scheme achieves the common component rate-distortion region in the case when the sources have a common component, while if a common component is not present (i.e. replaced with highly correlated functions of the two inputs) it improves upon existing achievable bounds. We show that as the block-length of the primary code is increased, the transmission rate required in the scheme decreases, reaches its minimum at some finite value and then increases. This phenomenon is not typically seen in traditional schemes used in multi-terminal source coding.

An Achievable Rate Region for the Three-User Interference Channel Based on Coset Codes

We consider the problem of communication over a three-user discrete memoryless interference channel (3-IC). The current known coding techniques for communicating over an arbitrary 3-IC are based on message splitting, superposition coding, and binning using independent and identically distributed (i.i.d.) random codebooks. In this paper, we propose a new ensemble of codes-partitioned coset codes (PCCs)-that possess an appropriate mix of empirical and algebraic closure properties. We develop coding techniques that exploit the algebraic closure property of PCC to enable interference alignment over general 3-IC. We analyze the performance of the proposed coding technique to derive an achievable rate region for the general discrete 3-IC. Additive and non-additive examples are identified for which the derived achievable rate region is the capacity, moreover, strictly larger than the current known largest achievable rate regions based on the i.i.d. random codebooks.

Nested lattice codes for arbitrary continuous sources and channels

In this paper, we show that nested lattice codes achieve the capacity of arbitrary continuous channels with or without non-causal state information at the transmitter. We also show that nested lattice codes are optimal for source coding with or without non-causal side information at the receiver for arbitrary continuous sources. We show the optimality of lattice codes for the Gelfand-Pinsker and Wyner-Ziv problems in their most general settings.

Polar codes for some multi-terminal communications problems.

It is shown that polar coding schemes achieve the known achievable rate regions for several multi-terminal communications problems including lossy distributed source coding, multiple access channels and multiple descriptions coding. The results are valid for arbitrary alphabet sizes (binary or non-binary) and arbitrary distributions (symmetric or asymmetric).

Abelian Group Codes for Channel Coding and Source Coding

In this paper, we study the asymptotic performance of Abelian group codes for the channel coding problem for arbitrary discrete (finite alphabet) memoryless channels as well as the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources. For the channel coding problem, we find the capacity characterized in a single-letter information-theoretic form. This simplifies to the symmetric capacity of the channel when the underlying group is a field. For the source coding problem, we derive the achievable rate-distortion function that is characterized in a single-letter information-theoretic form. When the underlying group is a field, it simplifies to the symmetric rate-distortion function. We give several illustrative examples. Due to the nonsymmetric nature of the sources and channels considered, our analysis uses a synergy of information-theoretic and group-theoretic tools.