The Three/Two Gaussian Parametric LDLC Lattice Decoding Algorithm and Its Analysis

Efficient Decoding of Low Density Lattice Codes

“…The key idea is to make use of the tail effect of Gaussian functions, i.e., if two Gaussian functions have very distant means, then the product of them is approximately 0. This fact allows us to approximate the Gaussian mixture by 2d − 2 Gaussian functions, without sorting as in [9] or exhaustive search as in [10]. Simulation results confirm that the performance of proposed decoder is the same as the best known one in [10], give the same number of iterations.…”

“…The operation ⌊·⌉ rounds a number to the closest integer. According to (6)- (10), the messages exchanged between variable and check nodes are continuous functions. In Sommer's implementation [1], each continuous message is quantized and represented by a vector of 1024 elements.…”

“…which is a Gaussian mixture of infinitely many components. To simplify (16), the authors in [10] replace each periodic Gaussian by only two Gaussians 1 with a mean value close to y k :f…”

“…This complicated operation dramatically slows down the whole decoding process. To reduce the decoding complexity, Gaussian approximation (GA)based decoders have been proposed in [8][9][10]. The basic idea is to approximate the messages exchanged between variable and check nodes by Gaussian functions.…”

“…Current approaches suggest to use the dominating Gaussian in the mixture, by sorting [9] or exhaustive search [10]. Even then, the computational complexity remains high, e.g., O(2 d ) in [10]. Since the value of d is commonly set to 7 [1], current GA-based LDLC decoders are slow for long codes.…”