Polar Coding for Fading Channels

A polar coding scheme for fading channels is proposed in this paper. More specifically, the focus is Gaussian fading channel with a BPSK modulation technique, where the equivalent channel could be modeled as a binary symmetric channel with varying cross-over probabilities. To deal with variable channel states, a coding scheme of hierarchically utilizing polar codes is proposed. In particular, by observing the polarization of different binary symmetric channels over different fading blocks, each channel use corresponding to a different polarization is modeled as a binary erasure channel such that polar codes could be adopted to encode over blocks. It is shown that the proposed coding scheme, without instantaneous channel state information at the transmitter, achieves the capacity of the corresponding fading binary symmetric channel, which is constructed from the underlying fading AWGN channel through the modulation scheme.Comment: 6 pages, 4 figures, conferenc

Polar Coding for Secure Transmission and Key Agreement

Wyner's work on wiretap channels and the recent works on information theoretic security are based on random codes. Achieving information theoretical security with practical coding schemes is of definite interest. In this note, the attempt is to overcome this elusive task by employing the polar coding technique of Ar{\i}kan. It is shown that polar codes achieve non-trivial perfect secrecy rates for binary-input degraded wiretap channels while enjoying their low encoding-decoding complexity. In the special case of symmetric main and eavesdropper channels, this coding technique achieves the secrecy capacity. Next, fading erasure wiretap channels are considered and a secret key agreement scheme is proposed, which requires only the statistical knowledge of the eavesdropper channel state information (CSI). The enabling factor is the creation of advantage over Eve, by blindly using the proposed scheme over each fading block, which is then exploited with privacy amplification techniques to generate secret keys.Comment: Proceedings of the 21st Annual IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC 2010), Sept. 2010, Istanbul, Turke

Polar codes and polar lattices for independent fading channels

In this paper, we design polar codes and polar lattices for i.i.d. fading channels when the channel state information is only available to the receiver. For the binary input case, we propose a new design of polar codes through single-stage polarization to achieve the ergodic capacity. For the non-binary input case, polar codes are further extended to polar lattices to achieve the egodic Poltyrev capacity, i.e., the capacity without power limit. When the power constraint is taken into consideration, we show that polar lattices with lattice Gaussian shaping achieve the egodic capacity of fading channels. The coding and shaping are both explicit, and the overall complexity of encoding and decoding is O(N log2 N)

Coding mechanisms for communication and compression : analysis of wireless channels and DNA sequencing

textThis thesis comprises of two related but distinct components: Coding arguments for communication channels and information-theoretic analysis for haplotype assembly. The common thread for both problems is utilizing information and coding theoretic principles in understanding their underlying mechanisms. For the first class of problems, I study two practical challenges that prevent optimal discrete codes utilizing in real communication and compression systems, namely, coding over analog alphabet and fading. In particular, I use an expansion coding scheme to convert the original analog channel coding and source coding problems into a set of independent discrete subproblems. By adopting optimal discrete codes over the expanded levels, this low-complexity coding scheme can approach Shannon limit perfectly or in ratio. Meanwhile, I design a polar coding scheme to deal with the unstable state of fading channels. This novel coding mechanism of hierarchically utilizing different types of polar codes has been proved to be ergodic capacity achievable for several fading systems, without channel state information known at the transmitter. For the second class of problems, I build an information-theoretic view for haplotype assembly. More precisely, the recovery of the target pair of haplotype sequences using short reads is rephrased as the joint source-channel coding problem. Two binary messages, representing haplotypes and chromosome memberships of reads, are encoded and transmitted over a channel with erasures and errors, where the channel model reflects salient features of highthroughput sequencing. The focus is on determining the required number of reads for reliable haplotype reconstruction.Electrical and Computer Engineerin

Space-Time Signal Design for Multilevel Polar Coding in Slow Fading Broadcast Channels

Slow fading broadcast channels can model a wide range of applications in wireless networks. Due to delay requirements and the unavailability of the channel state information at the transmitter (CSIT), these channels for many applications are non-ergodic. The appropriate measure for designing signals in non-ergodic channels is the outage probability. In this paper, we provide a method to optimize STBCs based on the outage probability at moderate SNRs. Multilevel polar coded-modulation is a new class of coded-modulation techniques that benefits from low complexity decoders and simple rate matching. In this paper, we derive the outage optimality condition for multistage decoding and propose a rule for determining component code rates. We also derive an upper bound on the outage probability of STBCs for designing the set-partitioning-based labelling. Finally, due to the optimality of the outage-minimized STBCs for long codes, we introduce a novel method for the joint optimization of short-to-moderate length polar codes and STBCs

Polar Codes and Polar Lattices for Independent Fading Channels

Abstract In this paper, we design polar codes and polar lattices for i.i.d. fading channels when the channel state information is only available to the receiver. For the binary input case, we propose a new design of polar codes through single-stage polarization to achieve the ergodic capacity. For the non-binary input case, polar codes are further extended to polar lattices to achieve the egodic Poltyrev capacity, i.e., the capacity without power limit. When the power constraint is taken into consideration, we show that polar lattices with lattice Gaussian shaping achieve the egodic capacity of fading channels. The coding and shaping are both explicit, and the overall complexity of encoding and decoding is O(N log 2 N )