Polarization phenomenon over any finite field Fq with size q being a power of a prime is considered. This problem is a generalization of the original proposal of channel polarization by Arıkan for the binary field, as well as its extension to a prime field by Şaşoğlu, Telatar, and Arıkan. In this paper, a necessary and sufficient condition of a matrix over a finite field Fq is shown under which...

This work is on fast encoding and decoding of polar codes. We propose and detail 8-bit and 16-bit parallel decoders that can be used to reduce the decoding latency of the successive-cancellation decoder. These decoders are universal and can decode flexible-rate and flexible-length polar codes. We also present fast encoders that can be used to increase the throughput of serially-implemented pola...

In this paper, we propose a coding scheme based on polar codes for empirical coordination of autonomous devices. We consider a two-node network with a noisy link in which the input and output signals have to be coordinated with the source and the reconstruction. In the case of strictly causal encoding, we show that polar codes achieve the empirical coordination region, provided that a vanishing...

Advanced coding has been widely used to accomplish the high-performance requirements of wireless communications. While adhering to the perspective on energy-spectral efficiency, channel coding is still promising. To deal with such challenge, research initiatives on the linear block error correcting codes have gained accelerating momentum. In this paper we introduce polar codes which have proven...

Polar codes asymptotically achieve the symmetric capacity of memoryless channels, yet their error-correcting performance under successive-cancellation (SC) decoding for short and moderate length codes is worse than that of other modern codes such as low-density parity-check (LDPC) codes. Of the many methods to improve the error-correction performance of polar codes, list decoding yields the bes...

Polar codes are novel and efficient error correcting codes with low encoding and decoding complexities. These codes have a channel dependent generator matrix which is determined by the code dimension, code length and transmission channel parameters. This paper studies a variant of the McEliece public key cryptosystem based on polar codes, called"PKC-PC". Due to the fact that the structure of po...

This paper proposes a generalization of the recently introduced Successive Cancellation Flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard Successive Cancellation (SC) decoding. To make such an approach effective, we first introduce the concept of higher-order bit-flips, and propose a new metr...

We construct concatenated capacity-achieving quantum codes for noisy optical quantum channels. We demonstrate that the error-probability of capacityachieving quantum polar encoding can be reduced by the proposed low-complexity concatenation scheme. OCIS codes: (270.5585); (270.5565).

In this paper, a polar code for the m-user multiple access channel (MAC) with binary inputs is constructed. In particular, Arıkan’s polarization technique applied individually to each user will polarize any m-user binary input MAC into a finite collection of extremal MACs. The extremal MACs have a number of desirable properties: (i) the ‘uniform sum rate’ of the original channel is not lost, (i...

Polar codes are recursive general concatenated codes. This property motivates a recursive formalization of the known decoding algorithms: Successive Cancellation, Successive Cancellation with Lists and Belief Propagation. This description allows an easy development of the first two algorithms for arbitrary polarizing kernels. Hardware architectures for these decoding algorithms are also describ...