In this paper we extend the relation between convolutional codes and linear systems over finite fields to certain commutative rings through first order representations . We introduce the definition of rings with representations as those for which these representations always exist, and we show that finite products of finite fields belong to this class. We develop the input/state/output represen...

Constructions of woven graph codes based on constituent convolutional codes are studied, and examples of woven convolutional graph codes are presented. Existence of codes satisfying the Costello lower bound on the free distance within a random ensemble of woven graph codes based on s-partite, s-uniform hypergraphs is shown, where s depends only on the code rate. Simulation results for Viterbi d...

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...

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 ...

This paper concerns to blind identification of a convolutional code with desired rate in a noiseless transmission scenario. To the best of our knowledge, blind estimation of convolutional code based on only the received bitstream doesn’t lead to a unique solution. Hence, without loss of generality, we will assume that the transmitter employs a non-catastrophic encoder. Moreover, we consider a c...

This chapter describes the main architectures proposed in the literature to implement the channel decoders required by the WiMax standard, namely convolutional codes, turbo codes (both block and convolutional) and LDPC. Then it shows a complete design of a convolutional turbo code encoder/decoder system for WiMax.

Recently a new construction of run length limited block error control codes based on control matrices of linear block codes was proposed. In this paper a similar construction for obtaining trellis run length limited error control codes from convolutional codes is described. The main advantage of it, beyond its simplicity is that it does not require any additional redundancy except the one which...

io-port 06440419 Chen, Jianzhang; Li, Jianping; Huang, Yuanyuan; Lin, Jie Some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes. Linear Algebra Appl. 475, 186-199 (2015). Summary: Quantum maximal-distance-separable (MDS) codes are an important class of quantum codes. Recently, many scholars utilize constacyclic codes to construct some quantum MDS code...