Good Index Choosing for Polarized Relay Channel

This paper will be discussed about the relay channels polarization in order to achieve more capacity region and will be shown that if the inputs of two different relay channels followed the Arikan's polarization structure, then one can categorized these channels to good channel and bad channel. Encoding and decoding complexity for these codes are like to original polar code, O (N.log⁡〖N)〗, and the error probability for them is O (〖2^(-(N) )〗^β ). As, a new scheme for choosing good indices for sending the information in polarized relay channel is presented. The relay channel, introduced by Van der Meulen in [1], is a communication channel and it has a sender and a receiver that assisted in communication by another way, which is a relay node. A memoryless relay channel is specified by probability distribution W(Y_r,Y|〖X,X〗_r ), where X is the transmitted symbol by the source, X_r is the transmitted symbol by the relay, Y_r is the received symbol by the relay and Y is the received symbol by the destination according to figure (1). One can assume that the message M is uniformly distributed over the message set and the average probability of error is defined as P_e^((n))=Pr{M ̂≠M}, where M is the estimation of decoder. Rate R is said to be achievable if there exist a sequence of 〖(2〗^NR,N) codes, N is the length of the code, such that 〖lim〗_(N→∞) P_e^((n))=0.