M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bull., vol. 66, pp.181-191, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....number generators (cf. 24] 26] and [50, pp. 89 101, 110] The finite region searched in these algorithms is a parallelepiped, with its axes parallel to the basis vectors. In general, the development of closest point algorithms follows two main branches, inspired by two seminal papers: Pohst [63] in 1981 examined lattice points lying inside a hypersphere, whereas Kannan [46] in 1983 used a rectangular parallelepiped. Both papers later appeared in revised and extended versions, Pohst s as [30] and Kannan s (following the work of Helfrich [42] as [47] The Pohst and Kannan strategies are ....

....in the row space of and one parallel to . The former is the dimensional decoding error while the length of the latter is . Since varies with , the upper bound can be chosen as (14) which is different for different layers in (13) The idea of letting depend on is the Pohst strategy [30] 62] [63], 78] 80] In geometrical terms, points inside a hypersphere, not a parallelepiped, are investigated. When any lattice point inside the sphere is found, the bound can be immediately updated to , since is an obvious upper bound on and . The Schnorr Euchner strategy, proposed in [67] combines ....

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bull., vol. 15, pp. 37--44, Feb. 1981.

....t #H, and the unitary matrix [c.f. 8) where # is unitary] # : we can rewrite (9) compactly as: y = H#s w. 10) Maximum likelihood (ML) decoding can be employed to detect s from y optimally regardless of N r , but possibly with high complexity. Sphere decoding (SD) [44,50,23] or See also [15,8,11] for related independent works semi definite programming [32] algorithms can also be used to achieve near optimal performance. The decoding complexity depends on the length of s, which here is N = N t . The SD algorithm is known to have average complexity ) 23] ....

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bull., vol. 15, pp. 37--44, Feb. 1981.

.... uL= arg,nMin II x II 2 = arg, n Min II II 2 (7) where n is the signal constellation. This is equivalent of searching the closest vector in lattice A (in the 2NTdimensional Euclidean space R NT) to the received vector x. Till now many algorithms have been proposed to solve this well known problem [7] [8] We modify the CPS algorithm, proposed in [6] to make this algorithm fast and low complex. just proportional to Ilwk, II 2, and thus the post detection SNRs are proportional to 1 llwk, II 2 wherew, is kith row of . Assuming that all components of s belong to the same constellation, s , ....

M. Pohst, "On the computation of lattice vectors of Minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bulletin, vol. 15, pp. 37-44, Feb. 1981

....algorithm. The complexity of ML decoding is O(M ) per symbol, or, O(NM ) per block, where M is the constellation size. The ML equalizer will thus be practical only when M and or L are relatively small. Another reduced complexity option for (near) ML detection is via sphere decoding (SD) [6], which is practical for ZP only transmissions with small block sizes. IV SIMULATION AND DISCUSSION To show the difference in performance, we depict in Figure 4 the BER SNR curves of various equalizers with parameters (N, L, P ) 64, 2, 66) The channel is of length L 1=3, with i.i.d. taps of ....

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bulletin, vol. 15, pp. 37--44, 1981.

....number generators (cf. 17, 18] and [30, pp. 89 101, 110] The finite region searched in these algorithms is a parallelepiped, with its axes parallel to the basis vectors. In general, the development of closest point algorithms follows two main branches, inspired by two seminal papers: Pohst [38] in 1981 examined lattice points lying inside a hypersphere, whereas Kannan [27] in 1983 used a rectangular parallelepiped. Both papers later appeared in revised and extended versions, Pohst s as [20] and Kannan s (following the work of Helfrich [25] as [28] The Pohst and Kannan strategies are ....

....decoding error while the length of the latter is yn . Since yn varies with un , the upper bound ae n Gamma1 can be chosen as ae n Gamma1 = p ae 2 n Gamma y 2 n (14) which is different for different layers in (13) The idea of letting ae n Gamma1 depend on un is the Pohst strategy [20, 37, 38, 49, 51]. In geometrical terms, points inside a hypersphere, not a parallelepiped, are investigated. When any lattice point x 0 inside the sphere is found, the bound ae n can be immediately updated to kx 0 Gamma xk, since kx 0 Gamma xk is an obvious upper bound on k x Gamma xk and kx 0 Gamma ....

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bulletin, vol. 15, pp. 37--44, Feb. 1981.

....nearest neighbor encoding in vector quantization are valid for any unstructured codebook. They do not take full advantage of the lattice structure which is useful for large bit rates. The algorithm described in section 3 was first created as building block of a general Minkowski s basis reduction [17, 14]. We have adapted it to allow the decoding of any general lattice. We may also observe here that, since any linear block code C over Z q (the ring of integers modulo q) is in a sense equivalent to a sublattice of Z n (see Construction A in [1, Chapter 5] any general decoding algorithm will ....

....hexagonal lattice. based on the dual of 3. A preliminary base reduction can restrict the size of the starting region, but the search becomes prohibitively complex when the lattice dimensionality grows above a certain threshold (around 10) A substantial improvement was introduced by Pohst in [14] and further analyzed in [17] We briefly illustrate this algorithm here, and provide some further insight through its geometrical interpretation. Consider a vector u 2 R d , and let kuk = p uu T denote its Euclidean norm. A ball of radius p C is defined by the inequality kuk 2 C: ....

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced basis with applications," ACM SIGSAM Bulletin, vol. 15, 1981, pp. 37--44.

No context found.

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bull., vol. 66, pp.181-191, 1994.

No context found.

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bull., vol. 66, pp. 181-191, 1994.

No context found.

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced basis with applications," ACM SIGSAM, vol. 15, pp. 37--44, 1981.

No context found.

M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," ACM SIGSAM Bull., vol. 66, pp.181-191, 1994.

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