Główne pojęcia
A coding scheme with scalar lattices can achieve the capacity region of K-receiver Gaussian vector broadcast channels with K independent messages by decomposing each receiver channel into parallel scalar channels with known interference and applying dirty paper coding with modulo interval, amplitude shift keying, and probabilistic shaping.
Streszczenie
The paper presents a capacity-achieving coding scheme for K-receiver Gaussian vector broadcast channels with K independent messages. The key steps are:
- Decompose each receiver channel into parallel scalar channels with known interference using noise whitening and singular value decomposition.
- Apply dirty paper coding with scalar lattices to each parallel scalar channel. This involves:
- Using a modulo interval, amplitude shift keying, and probabilistic shaping to encode the channel inputs.
- Treating the real and imaginary parts of the channel outputs as independent with the same channel gain and noise variance.
- By choosing large modulo intervals and amplitude shift keying alphabets, along with truncated Gaussian shaping, the achievable rate tuples can include all points inside the capacity region.
- The authors prove that the key lemmas and theorems from their previous work on dirty paper coding with scalar lattices remain valid in this more general setting with multiple receivers and non-Gaussian noise.
Statystyki
The power constraint requires the sum of the covariance matrices of the transmitted signals for each receiver to be less than or equal to the total transmit power constraint.
Cytaty
"Dirty paper coding (DPC) with scalar lattices can achieve the capacity of the dirty paper channel [1]; cf. [2], [3]. The result suggests that a similar scheme can achieve the capacity of multi-input, multi-output (MIMO) broadcast channels, and the purpose of this paper is to prove this."
"We may write Zk = Q1/2k Wk where the entries Wk,i of Wk are i.i.d. CSCG with unit variance. Thus, using (5), (8), and (10), we have ˜Zk = U†k ˇQ−1/2k [ P l>k HkK1/2l Vl ˜Xl ! + Q1/2k Wk ]."