Sure, most of you are aware that right now everyone is thinking or at least the industry and researchers about next generation, first generation what will 5G be, a significant part telecommunication standard has been finalised, in particular error control codes be used telecommunication. One called Low-Density Parity Check code (or LDPC for short), other Polar Code. These two famous celebrated ...

Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the corresponding code length is limited to the power of two. In this paper, we establish a systematic framework to design the rate-compatible punctured polar (RCPP) codes with arbitrary code length. A new theoretic tool, called polar spectra, is p...

We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update ...

Study of polar codes in fading channels is of great importance when applying polar codes in wireless communications. Channel estimation is a fundamental step for communication to be possible in fading channels. For both systematic and non-systematic polar codes, construction of them is based on an information set and the known frozen bits. Efficient implementation of systematic and non-systemat...

In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arıkan’s polarization technique applied individually to each user transforms independent uses of a m-user binary input MAC into successive uses of extremal MACs. This transformation has a number of desirable properties: (i) the ‘uniform sum rate’ of the original MAC is pr...

The generator matrices of polar codes and ReedMuller codes are submatrices of a Kronecker product of a lower-triangular binary square matrix. These submatrices are chosen according to an index set pointing to rows, which for polar codes minimize the Bhattacharyya parameter, and which for Reed-Muller codes maximize the Hamming weight. This work investigates the properties of this index set in th...

Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying ergodic finite ...

This paper studies polar coding for secure communications over the general two-way wiretap channel, where two legitimate users communicate with each other simultaneously while a passive eavesdropper overhears a combination of their exchanged signals. The legitimate users wish to design a coding scheme such that the interference between their codewords can be leveraged to jam the eavesdropper. T...