The main problem concerning the hardware implementation of turbo codes is the lack of parallelism in the MAP-based decoding algorithm. This paper proposes to overcome this problem with a new family of turbo codes, named Slice Turbo Codes. This family is based on two ideas: the encoding of each dimension with P independent tail-biting codes and a constrained interleaver structure that allows par...

space subcode of a Reed-Solomon (SSRS) code Over GF(2"') is the set of RS codewords, whose components all lie in a particular GF(2)subspace of GF(2"). SSRS codes include both generalized B C H codes and "trace-shortened" Rs codes [2][3] as special casea. In this paper we present an explicit formula for t h e dimension of an arbitrary RS subspace subcode. Using this formula, we And that in many ...

The geometric codes are the duals of the codes defined by the designs associated with finite geometries. The latter are generalized Reed-Muller codes, but the geometric codes are, in general, not. We obtain values for the minimum weight of these codes in the binary case, using geometric constructions in the associated geometries, and the BCH bound from coding theory. Using Hamada’s formula, we ...

Given two binary codes of length n, using Plotkin construction we obtain a code of length 2n. The construction works for linear and nonlinear codes. For the linear case, it is straightforward to see that the dimension of the final code is the sum of the dimensions of the starting codes. For nonlinear codes, the rank and the dimension of the kernel are standard measures of linearity. In this rep...

The geometric codes are the orthogonals of the codes defined by the designs associated with finite geometries. The latter are generalized Reed-Muller codes, but the geometric codes are, in general, not. We obtain values for the minimum weight of these codes in the binary case, using geometric constructions in the associated geometries, and the BCH bound from coding theory. Using Hamada’s formul...

This paper considers the performance of single parity check (SPC) multidimensional product codes in an Additive White Gaussian Noise channel. Asymptotic performance bounds are derived and compared to simulation results. A new code structure based on SPC product codes is introduced. This structure involves interleaving between the encoding of each dimension. Weight distribution analysis is used ...

A Z2Z4Q8-code is a non-empty subgroup of a direct product of copies of Z_2, Z_4 and Q_8 (the binary field, the ring of integers modulo 4 and the quaternion group on eight elements, respectively). Such Z2Z4Q8-codes are translation invariant propelinear codes as the well known Z_4-linear or Z_2Z_4-linear codes. In the current paper, we show that there exist"pure"Z2Z4Q8-codes, that is, codes that ...

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n − 1)dimensional projection being given. We give a number of examples, like a four-dimensional body of constant width whose 3D-projection is the classical Meissner’s body.