The thresholds obtained from the DE indicate that the TC ensembles from the unified ensemble have similar asymptotic behavior to the original TC ensembles.
While a recent construction by Calis and Koyluoglu generates $(r;s)$ PMDS codes for all $r$ and $s$, its field size is exponentially large.In this paper, a family of PMDS codes with field size $\mathcal\left( \max\^s \right)$ is presented.Since this construction uses well-developed convolutional constituent codes, we believe that it would be competitive to turbo codes in the future mobile communication systems.In this work, we adapt the notion of generalized Hamming weight of block codes to introduce the novel concept of generalized column distances for convolutional codes.In this work, we generalize the TM-MDS conjecture, and present an algebraic-combinatorial approach based on polynomial-degree reduction for proving this conjecture.
Our proof technique's strength is based primarily on reducing inherent combinatorics in the proof.
This can be considered an extension of the work done by J. York on the generalized Hamming weights for free distance of convolutional codes.
We also introduce the concept of Almost-MDP and Near- MDP convolutional code.
The first channel is a state-dependent semi-deterministic relay channel.
The CSI is available only at the transmitter and receiver, but not at the relay.
The bin index of the deterministic output is selected by the transmitter, such that the relay's transmission is coordinated with the states.