In this report, we review the construction of polar codes and we briefly present the main results that lead to the conclusion that polar codes are capacity achieving over binaryinput discrete memoryless channels. Moreover, we discuss a more sophisticated variant of successive cancellation decoding, namely list successive cancellation decoding, that aims to improve the finite-length performance ...

Introduction: Polar codes are a major breakthrough in coding theory [1]. They can achieve Shannon capacity with a simple encoder and a simple successive cancellation (SC) decoder, both with low complexity of the order of ( ) N N log O , where N is the code block size. But for short and moderate lengths, the error rate performance of polar codes with the SC decoding is not as good as LDPC or tur...

Polar codes are traditionally constructed by calculating the reliability of channels, then sorting them intensive calculations to select most reliable channels. However, these operations can be complicated especially when, polar code length, N becomes great. This paper proposes a new low-complexity procedure for construction over binary erasure and additive white Gaussian noise (AWGN) Using pro...

Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of nondegenerate hyperplane codes, in terms of the polar complex of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a non-degenerate hyperplane code is shellable and show that all cu...

This paper investigates polar codes for q-ary input channels using other kernels than [ 1 0 1 1 ] to construct the generator matrix. The kernel is optimized by maximizing the spread of the polar martingale and it is shown that in certain cases, the resulting construction has a significantly improved error probability (even at small block length like n = 1024).

The traditional fast successive-cancellation (SC) decoding algorithm can effectively reduce the steps, but adopts a sub-optimal algorithm, so it cannot improve bit error performance. In order to performance while maintaining low we introduce neural network subcode that achieve optimal and combine with SC algorithm. While exploring how node (NNN) R1, R0, single-parity checks (SPC), Rep, find fai...

We improve the method in [1] for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known successive decoding algorithms for polar codes. Overall rate and block length remain unchanged, the decoding complexity is at most doubled. A comparison to related methods f...