˗ Polar codes are provably capacity achieving linear block codes. The generator matrix of these codes is specified by knowing the parameters of transmission channel, length and dimension of the used code. On the other hand, for the cryptosystems based on general decoding problem (i.e. code based cryptosystems), the generator matrix of the applied code should be properly hidden from the attacker...

We present a concise description of Orthogonal Polar Grassmann Codes and motivate their relevance. We also describe efficient encoding and decoding algorithms for the case of Line Grassmannians and introduce some open problems.

A secret can be an encrypted message or a private key to decrypt the ciphertext. One of the main issues in cryptography is keeping this secret safe. Entrusting secret to one person or saving it in a computer can conclude betrayal of the person or destruction of that device. For solving this issue, secret sharing can be used between some individuals which a coalition of a specific number of them...

Gaussian approximation (GA) is widely used to construct polar codes. However when the code length is long, the subchannel selection inaccuracy due to the calculation error of conventional approximate GA (AGA), which uses a two-segment approximation function, results in a catastrophic performance loss. In this paper, new principles to design the GA approximation functions for polar codes are pro...

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...

The goal of channel coding is to detect and correct errors that appear during the transmission of information. In the past few decades, channel coding has become an integral part of most communications standards as it improves the energy-efficiency of transceivers manyfold while only requiring a modest investment in terms of the required digital signal processing capabilities. The most commonly...

The uni-polar orthogonal codes, with code length 'n' and code weight 'w' having auto-correlation and cross-correlation constraints equal to 1, can be designed with proposed algorithm. This proposed scheme design all the possible groups containing maximum number of orthogonal codes as per Johnson bounds. In this case, each of the designed groups is independent with other groups of uni-polar orth...

Cyclic redundancy check (CRC) aided polar codes are capable of achieving better performance than low-density parity-check (LDPC) codes under the successive cancelation list (SCL) decoding scheme. However, the SCL decoding scheme suffers from very high space and time complexities. Especially, the high space complexity is a major concern for adopting polar codes in modern mobile communication sta...

The polar codes are a class of linear block error-correcting codes transmitted over symmetric binaryinput discrete memoryless channels [1, 2, 3]. As their length N, N = 2n, increases, their performance tends to the Shannon limit. Subsequent publications (e.g., [4, 5]) have addressed practical aspects of the polar codes such as the size length, N, of a polar code that can support a specific feas...