A Unified Framework for Tree Search Decoding : Rediscovering the Sequential Decoder

TL;DR

This paper introduces a unified tree search decoding framework for lattice codes in Gaussian channels, combining preprocessing with MMSE-DFE and a generic branch-and-bound search to improve efficiency and performance.

Contribution

It presents a comprehensive tree search decoding framework that unifies existing sphere decoders and introduces a novel MMSE-Fano decoder with superior tradeoffs.

Findings

The MMSE-Fano decoder achieves excellent performance-complexity balance.

The framework encompasses all known sphere decoders as special cases.

Simulation results demonstrate improved decoding efficiency in MIMO and ISI scenarios.

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 {\em 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 MMSE-Fano decoder is established via simulation results and analytical arguments in several MIMO and ISI scenarios.