In this paper we introduce a new type of superregular matrices that give rise to novel constructions of two-dimensional (2D) convolutional codes with finite support. These codes are of rate 1/n and degree δ with n ≥ δ + 1 and achieve the maximum possible distance among all 2D convolutional codes with finite support with the same parameters.

This paper applies error exponent analysis the derivation of the distribution of error events in a convolutional code at the output of a Viterbi decoder. Even if the mean error behaviour of convolutional codes is a well known topic, however a precise analysis of the error events at the output of Viterbi decder is still lacking. The classical approach to derivation of the error events distributi...

Basic properties of a characteristic matrix for a tail-biting convolutional code are investigated. A tail-biting convolutional code can be regarded as a linear block code. Since the corresponding scalar generator matrix G has a kind of cyclic structure, an associated characteristic matrix also has a cyclic structure, from which basic properties of a characteristic matrix are obtained. Next, usi...

It has long been known that convolutional codes have a natural, regular trellis structure that facilitates the implementation of Viterbi's algorithm [30,10]. It has gradually become apparent that linear block codes also/]ave a natural, though not in general a regular, "minimal" trellis structure, which allows them to be decoded with a Viterbi-1ike algorithn] [2,31,22,11,27,14,12,16,24,25,8,15]....

Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible. It has been shown that, transmitting over an erasure channel, these codes have optimal recovery rate for windows of a certain length. Reverse MDP convolutional codes have the additional advantage that they are suitable for forward and backward decoding algorithms. Beyond th...

A general description of convolutional codes is provided by a set of linear equations called discrete-time state-space equations in control theory. We discuss how the notions of controllability, observability and minimality in control, are applied to convolutional code design. The notion of output-observability is used to ensure minimality of a convolutional code. Without concatenation, searchi...

In digital communication forward error correction methods have a great practical importance when channel is noisy. Convolutional error correction code can correct both type of errors random and burst. Convolution encoding has been used in digital communication systems including deep space communication and wireless communication. The error correction capability of convolutional code depends on ...

In this paper we discuss AWGN coding theorems for ensembles of coding systems which are built from fixed convolutional codes interconnected with random interleavers. We call these systems “turbo-like” codes and they include as special cases both the classical turbo codes [1,2,3] and the serial concatentation of interleaved convolutional codes [4]. We offer a general conjecture about the behavio...

In digital communication, convolutional codes are important to control the errors between the transmitter and receiver. Convolutional code is a type of error correction code (ECC) which can perform both error detection and correction operation between transmitter and receiver side. Here information bits are transformed serially through the architecture which is one of the major advantages as co...