The Final Case of the Decoding Delay Problem for Maximum Rate Complex Orthogonal Designs

On the Minimum Decoding Delay of Balanced Complex Orthogonal Designs

“…It's clear that both (1), (2), (3) are true for each B j form. Since G can be transformed into B j by column-restricted operations, and (1),(2),(3)are invariant under column-restricted operations, we conclude that G satisfies (1),(2) and(3).…”

“…It's impossible to optimize all the design considerations simultaneously for general n. For the rate, Liang [9] proves a tight upper bound, which is slightly greater than 1/2 depending on n. When the rate is maximized, Adams et al proves a lower bound on the decoding delay, which grows factorially in n [2,3]. Furthermore, Kan and Li [8] give a complete classification of "first type" CODs, which are those without submatrices ±z j 0 0 ±z * j and ±z * j 0 0 ±z j , which contains all the CODs with maximum rate.…”

On the criteria for designing complex orthogonal space-time block codes

“…Based on this concept, Liang [8] solved the maximum-rate problem. The minimum decoding delay problem was solved by Adams et al [10,11]. Their proof is based on the concept of zero pattern.…”

“…If the rate of G reaches the upper bound, then the tight lower bound of p is 2m m+1 if n ≡ 0, 1, 3 mod 4 [10], and 2 2m m+1 otherwise [11]. A COD G[p, n, k] is said to be atomic if any submatrix consisting of some but not all rows of G is not a COD.…”

“…Liang [8] and Su et al [16] presented a class of conjugation-separated maximum-rate CODs independently, which reaches the minimum decoding delay if the number of columns n ≡ 1, 2, 3 mod 4 [10,11]. This simply implies the following corollary.…”