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Table 5 Relationship between different distributed RS codes and optimized selection patterns

From: Jointly optimized design of distributed RS-coded spatial modulation by appropriate selection at the relay

No.

Distributed RS codes

Optimized selection patterns

\(\varvec{RS_1 (N,K_1)}\)

\(\varvec{RS_2 (N,K_2)}\)

\(\varvec{\upeta }^{\varvec{(1)}}\)

\(\varvec{\upeta }^{\varvec{(2)}}\)

1

\(RS_1(15,13)\)

\(RS_2 (15,7)\)

\(\qquad \quad [1\quad 3\quad 5\quad 8\quad 9 \quad 11\quad 12]\)

\(\qquad [3\quad 5\quad 7\quad 9\quad 10\quad 11\quad 12]\)

2

\(RS_1(31,25)\)

\(RS_2 (31,13)\)

–

\([2\quad 3\quad 4\quad 6\quad 8\quad 9\quad 10\quad 13 \quad 15\quad 16\quad 17\quad 19\quad 22]\)

3

\(RS_1(63,61)\)

\(RS_2 (63,41)\)

–

\([1\quad 2 \quad 4\quad 5\quad 6 \quad 7\quad 9\quad 10\quad 12\quad 13 \quad 14 \quad 16\quad 17 \quad 19 \quad 21\)

    

\(23\quad 24\quad 25\quad 27\quad 29 \quad 30\quad 32\quad 33\quad 35\quad 37\quad 38\quad 39\quad 41\)

    

\(42\quad 43\quad 46\quad 47\quad 49\quad 51\quad 52\quad 54\quad 57\quad 58\quad 59\quad 60\quad 61]\)