Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelhol...

An improved upper bound on the error probability (first error event) of time-invariant convolutional codes, and the resulting error exponent, is derived in this paper. The improved error bound depends on both the delay of the code and its width (the number of symbols that enter the delay line in parallel) . Determining the error exponent of time-invariant convolutional codes is an open problem....

Turbo equalizers have been shown to be successful in mitigating the effects of inter-symbol interference introduced by partial response modems and by dispersive channels for code rates of 1 2. In this contribution, we comparatively studied the performance of a range of binary phase-shift keying turbo equalizers employing block-turbo codes, namely Bose–Chaudhuri–Hocquenghen turbo codes, convolut...

A matrix embedding code was developed as a commonly used steganographic technique in which a parity-check matrix is used to perform embedding. However, a drawback of high decoding complexity for linear block codes by using the maximum-likelihood algorithm is unrealistic. This paper proposes a simple and effective trellis embedding scheme for binary messages. Compared with a matrix embedding alg...

In this paper, we investigate the performance-complexity tradeoff of convolutional codes for broadband fixed wireless access systems by considering the effects of quantization and path metric memory in practical Viterbi decoding implementations. We show that in systems with limited antenna diversity, low memory codes achieve a better error-rate performance compared to that of high memory codes....

Most design approaches for trellis-coded quantization take advantage of the duality of trellis-coded quantization with trellis-coded modulation, and use the same empiricallyfound convolutional codes to label the trellis branches. This letter presents an alternative approach that instead takes advantage of maximum-Hamming-distance convolutional codes. The proposed source codes are shown to be co...

In this article, we will study a class of concatenated coding communications systems that is built from convolutional codes and interleavers. These systems include as special cases both the classical turbo codes [1,2] and the serial concatenation of convolutional codes [4]. Our main results are a method for computing a conjectured interleaving gain exponent and for optimizing the effective free...

Analytic expressions for the exact probability of erasure for systematic, rate-1/2 convolutional codes used to communicate over the binary erasure channel and decoded using the soft-input, soft-output (SISO) and a posteriori probability (APP) algorithms are given. An alternative forward-backward algorithm which produces the same result as the SISO algorithm is also given. This low-complexity im...

In this paper, we consider a class of column-weight two quasi-cyclic low-density parity check codes in which the girth can be large enough, as an arbitrary multiple of 8. Then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. Finally, we show that the free distance of the convolutio...

The product code proposed in this chapter is constructed by using time-invariant convolutional code. Its component codes’ trellis structure does not vary in time as in product codes constructed with Hamming, BCH, and Reed Solomon block codes. Moreover, the number of states in the trellis structure of a block code may grow exponentially with the difference of codeword and data block lengths, whe...