A unified framework for tree search decoding: rediscovering the sequential decoder

Abstract

We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopted. In our framework, the CLPS algorithm decomposes into the preprocessing and tree search stages. The role of the preprocessing stage is to expose the tree structure in a form matched to the search stage. We argue that the minimum mean square error decision feedback (MMSE-DFE) frontend is instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSE-DFE filtering allows for using lattice reduction methods to reduce complexity, at the expense of a marginal performance loss, and solving under-determined linear systems. For the search stage, we present a generic method, based on the branch and bound (BB) algorithm, and show that it encompasses all existing sphere decoders as special cases. The proposed generic algorithm further allows for an interesting classification of tree search decoders, sheds more light on the structural properties of all known sphere decoders, and inspires the design of more efficient decoders. In particular, an efficient decoding algorithm that resembles the well known Fano sequential decoder is identified. The excellent performance-complexity tradeoff achieved by the proposed MMSEFano decoder is established via simulation results and analytical arguments in several MIMO and ISI scenarios.

Effective reduction for sphere decoder in linear multi-input multi-output channel systems

“…The Gaussian linear MIMO channel system can be written as the following real model (see [5]) When the matrix A has full row rank, various generalised SD (GSD) algorithms were proposed to attack (2) (see, e.g. [15 -20]).…”

A Low-Complexity Soft-MIMO Detector Based on the Fixed-Complexity Sphere Decoder

“…The FSD, analogously to the sphere decoder (SD), can be seen as a constrained tree search through a tree with M levels where P branches originate from each node [12]. The FSD performs a fixed two-stage constrained tree search, from i = M to i = 1, depending on a parameter T .…”

Radius selection for lattice sphere decoder-based block data transmission systems

“…8 for every x k 2 Z because this would require an exhaustive computational complexity equal to the original brute force ML approach. Instead, a constrained tree search can be used to find all possible solutions inside the sphere [10,11]. Therefore, the aim of Eqs.…”