Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based on analogies with model predictive optimal control, we propose a new iterative method for convolutional decoding that is cheaper to implement than establish...

In this paper we address the problem of decoding 2D convolutional codes over the erasure channel. To this end we introduce the notion of balls around a burst of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main idea is to reduce the decoding problem of 2D convolutional codes to a problem of decoding a set of associate...

Abstract — In this paper, we propose a novel method to construct low rate recursive convolutional codes. The ‘overall’ convolutional code has a block code and a simple recursive convolutional code as building blocks. The novelty of this type of convolutional code is that it uses coset leaders in order to distinguish the signals that originate from different states. Several of these codes are th...

We show that the state complexity profile of a convolutional code is the same as that of the reciprocal of the dual code of in case that minimal encoders for both codes are used. Then, we propose an optimum permutation for any given ( 1) binary convolutional code that will yield an equivalent code with the lowest state complexity. With this permutation, we are able to find many ( 1) binary conv...

This paper revisits strongly-MDS convolutional codes with maximum distance profile (MDP). These are (non-binary) convolutional codes that have an optimum sequence of column distances and attains the generalized Singleton bound at the earliest possible time frame. These properties make these convolutional codes applicable over the erasure channel, since they are able to correct a large number of...

Convolutional neural networks (CNNs) are biologically-inspired variants of multi-layer perceptrons (MLPs). In biology, a visual cortex contains a complex arrangement of cells. These cells are sensitive to small subregions of the visual field. Inspired by the structure of visual cortices and cells, the notion of receptive fields and local filters are introduced as a core component of convolution...

Resumo Maximum Distance Separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Zpr was recently discovered in [26] via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Zpr from a new perspectiv...

In this lecture we discuss construction of signals via a trellis. That is, signals are constructed by labeling the branches of an infinite trellis with signals from a small set. Because the trellis is of infinite length this is conceptually different than the signals created in the previous chapter. We the codes generated are linear (the sum of any two sequences is also a valid sequence) then t...

Abstract – In this paper a formal theory, construction methods, and a random ensemble approach for low-density parity-check convolutional codes (including turbo-codes) are presented. The principles of iterative decoding of low-density parity-check (LDPC) convolutional codes are given, and an iterative algorithm for decoding of homogeneous LDPC convolutional codes is described. Some simulation r...

Turbo code is recommended as a channel coding scheme, which has been shown to be capable of performing close to the Shannon Limit. In this paper, we compare the performance of both convolutional and block turbo codes over AWGN and Rayleigh fading channels. It is observed that the performance of convolutional turbo code is slightly better in the water fall region and the coding gain ranges from ...