On Space-Time Code Design With a Conditional PIC Group Decoding

Space-time code designs based on a partial interference cancellation (PIC) group decoding have been recently proposed. The PIC group decoding complexity depends on the group size and is between the lowest linear receiver complexity and the highest ML decoding complexity. The symbol rate for a space-time code achieving full diversity with the PIC group decoding is also between those for the linear receivers and the ML decoding. In this paper, we propose a new decoding, called conditional PIC group decoding, that is between the PIC group decoding and the ML decoding. With the proposed new decoding, we obtain a new design criterion for space-time codes to achieve full diversity, which is also between the one with the PIC group decoding and the one with the ML decoding. We then present some designs that satisfy the new criterion and in the meantime have higher symbol rates than that for the PIC group decoding.

I. Introduction

Full diversity achieving space-time code designs with low complexity decodings include orthogonal space-time codes (OSTC) [1]–[7], quasi OSTC type codes with simplified ML decoding [8]–[16], extended OSTC with conditional ML detection [17]–[20], codes with linear receivers [21]–[25], and codes with PIC group decoding [26], [28]. Due to the orthogonality constraint, the symbol rates for OSTC type codes decrease to [4] when the number of transmit antennas gets large. When the orthogonality is relaxed so that the full diversity can be achieved with linear receivers, the symbol rates can still be close to 1 when the number of transmit antennas gets large [23]. When the linear receiver is generalized/relaxed to the PIC group decoding, the symbol rates for full diversity achieving codes can be increased to be more than 1 but upper bounded by the group size [26]. It is known that the symbol rates for full diversity codes with the ML decoding can be full, i.e., , for transmit antennas [29]–[33], including perfect codes [31], [32]. A natural question is whether there are full diversity achieving codes with symbol rates higher than that with the PIC group decoding, and with a decoding of a lower complexity than the ML decoding.