On "Bit-Interleaved Coded Multiple Beamforming"

On “Bit-Interleaved Coded Multiple Beamforming” E. Akay 1 , H. J. Park 2 , E. Ayanoglu 2 A BSTRACT The interleaver design criteria described i n [1] shou ld take into account all error patterns of interest. In [1], let S be the number of streams employed and let α s be the number of times the stream s is employed with a corresponding channe l bit equal to 1 in an erro r path. Then, th e interleaver design criteria for single-carrier systems at the beginning of Secti on II of [1] should be as follows For all error paths of interest, 1) the consecutive coded bits are mapped over different symbols, 2) α s ≥ 1 for 1 ≤ s ≤ S. These criteria provide a sufficient conditio n for the Bit-Interleaved Coded Multiple Beamforming (BICMB) system of [1] to achieve full dive rsity as the subsequent analysis in [1] shows by replacing d free with the Hamming distance d H of that errored codeword with the all- zeros codeword. The interleaver design criteria in Se ction III of [1] should, similarly, be For all error paths of interest, 1) the consecutive coded bits are mapped over different symbols, 2) transmitted over different subcar riers of an OFDM symbol, 3) α s ≥ 1 for 1 ≤ s ≤ S. For both interleaver design cr iteria above, if the condition α s ≥ 1 is violated for any s, 1 ≤ s ≤ S, then that particular erro r pattern can dominate and the full diversity of the re sulting BICMB system is not guaranteed. It can be shown that for the 2x2 BICMB system w ith the industry standard (133, 171), code rate R=1/2, constraint length K=7 convolutional code, employing S = 2 streams, it is possible to come up with an interleaver that satisfies the interleaver design criteria above for all possible error patterns. R EFERENCES [1] E. Akay, E. Sengul, E. Ayanoglu, “Bit -Interleaved Coded Mul tiple Beamforming,” IEEE Transactions on Communications, Vol. 55, pp. 1802-1811, September 2007. 1 Atheros C ommunications, Inc., Santa C lara, CA 9505 4-3644. 2 Department of EECS, University of California, CA 92697-2625.