Yamada, Harashima, and Miyakawa proposed to use a trellis constructed based on a syndrome former for the purpose of Viterbi decoding of rate-(n − 1)/n convolutional codes. In this paper, we extend their code-trellis construction to general rate-k/n convolutional codes. We show that the extended construction is equivalent to the one proposed by Sidorenko and Zyablov. Moreover, we show that the p...

In this paper we will discuss isometries and strong isometries for convolutional codes. Isometries are weight-preserving module isomorphisms whereas strong isometries are, in addition, degree-preserving. Special cases of these maps are certain types of monomial transformations. We will show a form of MacWilliams Equivalence Theorem, that is, each isometry between convolutional codes is given by...

Space-time convolutional codes have shown considerable promise for providing improved performance for wireless communication through combined diversity and coding gain. However, systematic design procedures for space-time convolutional codes have not yet been developed. To date, the few existing example space-time codes have been developed using hand design. Systematic design procedures are pre...

In this paper we compare the decoding latency, i.e., the delay between the time a channel symbol is received and the time it is decoded, of block and convolutional codes. In particular, we compare low density parity check (LDPC) block codes with iterative message-passing decoding to convolutional codes with Viterbi decoding and stack sequential decoding. On the basis of simulations, we show tha...

| A tutorial introduction to the new class of binary parallel concatenated recursive systematic convolutional codes termed turbo codes is presented. It is shown that such codes are in fact linear block codes, and the encoding operation can be viewed as a modulo-2 multiplication of the information sequence with a generator matrix. A framework for analyzing the performance of turbo codes is propo...

In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)’s. These new AQCC’s are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which are also constructed here. The new codes have noncatastrophic generator matrices and they have great asymmetry. Since our constructions are performed algebrai...

New properties of q-ary cyclotomic cosets modulo n = qm − 1, where q ≥ 3 is a prime power, are investigated in this paper. Based on these properties, the dimension as well as bounds for the designed distance of some families of classical cyclic codes can be computed. As an application, new families of nonbinary Calderbank-Shor-Steane (CSS) quantum codes as well as new families of convolutional ...

Suggested reference for convolutional codes : “Fundamentals of Convolutional Coding” by Rolf Johannesson and Kamil Zigangirov, IEEE Press, 1999. An encoder for a binary block code takes a block of information bits and converts it into a block of transmitted bits (a codeword). A binary convolutional encoder takes a stream of information bits and converts it into a stream of transmitted bits, usi...

LDPC convolutional codes, also known as spatially coupled LDPC codes, have attracted considerable attention due to their promising properties. By coupling the protographs from different positions into a chain and terminating the chain properly, the resulting convolutional-like LDPC code ensemble is able to produce capacityachieving performance in the limit of large parameters. In addition, opti...