Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo--Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr--Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.

We propose novel lattice coding/decoding schemes for half-duplex outage-limited cooperative channels. These schemes are inspired by the cooperation protocols of Azarian et al. and enjoy an excel-lent performance-complexity tradeoff. More specifically, for the relay channel, we first use our lattice coding framework to generalize Yang and Belfiore implementation of the non-orthogonal amplify and forward cooperation protocol. This generalization is shown to offer significant performance gains while keeping the decoding complexity manageable. We then devise a novel variant of the dynamic decode and forward protocol, along with a lattice-coded implementation, which enjoys a near-optimal diversity-multiplexing tradeoff with a low encoding/decoding complexity. Finally, for the coopera-tive multiple-access channel, we present a lattice-coded implementation of the non-orthogonal amplify and forward protocol and demonstrate its excellent performance-complexity tradeoff. Throughout the paper, we establish the performance gains of our proposed protocols via a comprehensive simulation study. 1 Keywords: Lattice coding, lattice decoding, half-duplex channels, tree search, MMSE-Fano decoder, amplify and

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We give an extension of the work of Trott et al. on rotationally invariant codes and the work of Adler et al. and Marcus on constrained codes, to constrained codes invariant by a permutative map. A constructive proof is given of the existence a finite-state invertible phi-invariant code from arbitrary n-ary sequences to a phi-invariant so c system at constant rate 1 : 1 provided that phi is a permutative conjugacy of the sofic channel and that the Shannon capacity of the channel exceeds the capacity of the source. In the case of equality of the capacities of the source and of the phi-invariant channel, the same result holds when the permutative map has no bi-infinite fixed point which is a direct extension of the result of Trott et al. for the rotational case. The decoders can be made both sliding block, or "state independent", and phi-invariant.