Elementary information about convolutional codes over finite fields is introduced, and various motivations for extension to convolutional codes over finite rings are discussed. The recent primary motivation is found to be for use over phase modulation signals. Such ring codes enjoy the special property of phase weight equal to phase distance equal to the squared Euclidean distance between phase...

.’ parallel concatenated convolutional coding scheme consists of two constituent systematic convolutional encoders linked by an interleaver. The information bits at the input of the first encoder are scrambled by the interleaver before entering the second encoder. The codewords of the parallel concatenated code consist of the information bits followed by the parity check bits of both encoders. ...

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 this paper, we revisit the forward, backward and bidirectional Bahl-Cocke-Jelinek-Raviv (BCJR) soft-input soft-output (SISO) maximum a posteriori probability (MAP) decoding process of rate-1 binary convolutional codes. From this we establish some interesting explicit relationships between encoding and decoding of rate-1 convolutional codes. We observe that the forward and backward BCJR SISO ...

|In this work we studied the performance of the hybrid type-II Automatic Repeat reQuest (ARQ) system on Rayleigh fading channels. This system is based on High Rate Optimized Rate Compatible Punctured Convolutional (HRO-RCPC) codes combined with simple repetition codes. The performance is investigated for di erent packet sizes and constraint lengths of the convolutional encoder. Additionally the...

A popular combination in modern coding system is the convolutional encoder and the Viterbi decoder [5]. With a proper design, they can jointly provide an acceptable performance with feasible decoding complexity. In such a combination, a tradeoff on the error performance and the decoding complexity resides on the choice of the code constraint length. Specifically, the probability of Viterbi deco...

A fundamental problem of coding theory is the e cient decoding of certain classes of convolutional codes. It would be highly desirable to develop e cient algorithms which are capable of decoding classes of convolutional codes with particular algebraic properties. In this article we do formulate the problem in terms of linear systems theory and we show that the posed question is connected to som...

Convolutional codes have been widely used in several kinds of communication systems because of its excellent coding gain. Recently, the coded TPSK (Ternary phase shift keying) scheme has been proposed and it was shown that the scheme has attractive features for mobile communication systems; excellent bit error characteristics and small amount of amplitude fluctuation. The latter feature is very...

Turbo codes, in the form of parallel concatenated convolutional codes, consist of two recursive systematic convolutional encoders separated by an interleaver. Due to the presence of the interleaver, each constituent convolutional encoder accepts as input a block of information bits with a size equal to that of the interleaver rather than a continuous stream of information bits. By determining t...