A Novel Interleaving Scheme for Polar Codes

It's known that the bit errors of polar codes with successive cancellation (SC) decoding are coupled. We call the coupled information bits the correlated bits. In this paper, concatenation schemes are studied for polar codes (as inner codes) and LDPC codes (as outer codes). In a conventional concatenation scheme, to achieve a better BER performance, one can divide all $N_l$ bits in a LDPC block into $N_l$ polar blocks to completely de-correlate the possible coupled errors. In this paper, we propose a novel interleaving scheme between a LDPC code and a polar code which breaks the correlation of the errors among the correlated bits. This interleaving scheme still keeps the simple SC decoding of polar codes while achieves a comparable BER performance at a much smaller delay compared with a $N_l$-block delay scheme

Design and optimization of joint iterative detection and decoding receiver for uplink polar coded SCMA system

SCMA and polar coding are possible candidates for 5G systems. In this paper, we firstly propose the joint iterative detection and decoding (JIDD) receiver for the uplink polar coded sparse code multiple access (PC-SCMA) system. Then, the EXIT chart is used to investigate the performance of the JIDD receiver. Additionally, we optimize the system design and polar code construction based on the EXIT chart analysis. The proposed receiver integrates the factor graph of SCMA detector and polar soft-output decoder into a joint factor graph, which enables the exchange of messages between SCMA detector and polar decoder iteratively. Simulation results demonstrate that the JIDD receiver has better BER performance and lower complexity than the separate scheme. Specifically, when polar code length N=256 and code rate R=1/2 , JIDD outperforms the separate scheme 4.8 and 6 dB over AWGN channel and Rayleigh fading channel, respectively. It also shows that, under 150% system loading, the JIDD receiver only has 0.3 dB performance loss compared to the single user uplink PC-SCMA over AWGN channel and 0.6 dB performance loss over Rayleigh fading channel

Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels

A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity $I(W)$ of any given binary-input discrete memoryless channel (B-DMC) $W$. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of $N$ independent copies of a given B-DMC $W$, a second set of $N$ binary-input channels $\{W_N^{(i)}:1\le i\le N\}$ such that, as $N$ becomes large, the fraction of indices $i$ for which $I(W_N^{(i)})$ is near 1 approaches $I(W)$ and the fraction for which $I(W_N^{(i)})$ is near 0 approaches $1-I(W)$. The polarized channels $\{W_N^{(i)}\}$ are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC $W$ with $I(W)>0$ and any target rate $R < I(W)$, there exists a sequence of polar codes $\{{\mathscr C}_n;n\ge 1\}$ such that ${\mathscr C}_n$ has block-length $N=2^n$, rate $\ge R$, and probability of block error under successive cancellation decoding bounded as P_{e}(N,R) \le \bigoh(N^{-\frac14}) independently of the code rate. This performance is achievable by encoders and decoders with complexity $O(N\log N)$ for each.Comment: The version which appears in the IEEE Transactions on Information Theory, July 200

How to Achieve the Capacity of Asymmetric Channels

We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances in coding for symmetric channels help provide more efficient solutions for the asymmetric case. We consider, in more detail, three basic coding paradigms. The first one is Gallager's scheme that consists of concatenating a linear code with a non-linear mapping so that the input distribution can be appropriately shaped. We explicitly show that both polar codes and spatially coupled codes can be employed in this scenario. Furthermore, we derive a scaling law between the gap to capacity, the cardinality of the input and output alphabets, and the required size of the mapper. The second one is an integrated scheme in which the code is used both for source coding, in order to create codewords distributed according to the capacity-achieving input distribution, and for channel coding, in order to provide error protection. Such a technique has been recently introduced by Honda and Yamamoto in the context of polar codes, and we show how to apply it also to the design of sparse graph codes. The third paradigm is based on an idea of B\"ocherer and Mathar, and separates the two tasks of source coding and channel coding by a chaining construction that binds together several codewords. We present conditions for the source code and the channel code, and we describe how to combine any source code with any channel code that fulfill those conditions, in order to provide capacity-achieving schemes for asymmetric channels. In particular, we show that polar codes, spatially coupled codes, and homophonic codes are suitable as basic building blocks of the proposed coding strategy.Comment: 32 pages, 4 figures, presented in part at Allerton'14 and published in IEEE Trans. Inform. Theor

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201