An analysis is made of Maximum Likelihood Decoding (MLD) in a wireless Space Division Multiplexing (SDM) link, where information is transmitted and received simultaneously over several transmit and receive antennas to achieve large data rates and high spectral efficiencies. It is proven that maximum likelihood decoding obtains a diversity order equal to the number of receive antennas, independe...

The goal of the present paper is the derivation of a framework for the finite-length analysis of message-passing iterative decoding of low-density parity-check codes. To this end we introduce the concept of graph-cover decoding. Whereas in maximum-likelihood decoding all codewords in a code are competing to be the best explanation of the received vector, under graph-cover decoding all codewords...

This paper describes two freely available convolutional decoders written in the C language. One implements the Fano algorithm for sequentially decoding three rate l/2 K=32 codes while the other implcmcnts the Viterbi algorithm for maximum likelihood decoding of the rate l/2 K=7 NASA Standard code. Both support 8-W soft-decision decoding with arbitrary metric tables and perform according to theory.

In this paper we investigate the structure of the fundamental polytope used in the Linear Programming decoding introduced by Feldman, Karger and Wainwright. We begin by showing that for expander codes, every fractional pseudocodeword always has at least a constant fraction of non-integral bits. We then prove that for expander codes, the active set of any fractional pseudocodeword is smaller by ...

In this paper we focus our attention on a family of finite geometry codes, called type-I projective geometry low-density parity-check (PGLDPC) codes, that are constructed based on the projective planes PG(2, q). In particular, we study their minimal codewords and pseudo-codewords, as it is known that these vectors characterize completely the code performance under maximum-likelihood decoding an...

In his thesis, Wiberg showed the existence of thresholds for families of regular low-density parity-check codes under min-sum algorithm decoding. He also derived analytic bounds on these thresholds. In this paper, we formulate similar results for linear programming decoding of regular low-density parity-check codes.

In this report we consider some aspects of the general problem of encoding and decoding for time-discrete, amplitude-continuous memoryless channels. The results can be summarized under three main headings. 1. Signal Space Structure: A scheme for constructing a discrete signal space, for which sequential encoding-decoding methods are possible for the general continuous memoryless channel, is des...