Polar Codes for Arbitrary DMCs and Arbitrary MACs

Polar codes for Arbitrary DMCs

Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with “usual” polar codes, the block error probability under successive cancellation decoding is o(2−N 1/2− ), where N is the block length. The encoding and decoding in this coding scheme can be implemented with a complexity of O(N logN). It is shown that the same techn...

CBC MACs for Arbitrary-Length Messages: The Three-Key Constructions

Fast Polar Decomposition of an Arbitrary Matrix

The polar decomposition of an m x n matrix A of full rank, where rn n, can be computed using a quadratically convergent algorithm of Higham SIAMJ. Sci. Statist. Comput., 7 (1986), pp. 1160-1174]. The algorithm is based on a Newton iteration involving a matrix inverse. It is shown how, with the use of a preliminary complete orthogonal decomposition, the algorithm can be extended to arbitrary A. ...

Skew cyclic codes of arbitrary length

In this paper we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalization of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without ...

Double Cylinder Cycle codes of Arbitrary Girth

A particular class of low-density parity-check codes referred to as cylinder-type BC-LDPC codes is proposed by Gholami and Eesmaeili. In this paper We represent a double cylinder-type parity-check matrix H by a graph called the block-structure graph of H and denoted by BSG(H). Using the properties of BSG(H) we propose some mother matrices with column-weight two such that the rate of correspondi...