Algebraic space–time coding allows for reliable data exchange across fading multiple-input multiple-output channels. A powerful technique for decoding space–time codes is Maximum-Likelihood (ML) decoding, but well-performing and widely-used codes such as the Golden code often suffer from high ML-decoding complexity. In this article, a recursive algorithm for decoding general algebraic space–tim...

Iterat ive decoding is a widely used technique in modern communications systems. The Low Density Parity Check (LDPC) codes of Gallager were the earliest codes for which iterat ive decoding techniques were dēned. These codes along with a simple iterat ive decoding algorithm were int roduced in the r̄st part of this art icle. Here we describe a probabilist ic iterat ive decoding scheme, also propo...

To gain a better understanding of how neural ensembles communicate and process information, neural decoding algorithms are used to extract information encoded in their spiking activity. Bayesian decoding is one of the most used neural population decoding approaches to extract information from the ensemble spiking activity of rat hippocampal neurons. Recently it has been shown how Bayesian decod...

Many fundamental questions in theoretical neuroscience involve optimal decoding and the computation of Shannon information rates in populations of spiking neurons. In this paper, we apply methods from the asymptotic theory of statistical inference to obtain a clearer analytical understanding of these quantities. We find that for large neural populations carrying a finite total amount of informa...

We consider Linear Programming (LP) decoding of a fixed Low-Density Parity-Check (LDPC) code over the Binary Symmetric Channel (BSC). The LP decoder fails when it outputs a pseudo-codeword which is not a codeword. We design an efficient algorithm termed the Instanton Search Algorithm (ISA) which, given a random input, generates a set of flips called the BSC-instanton. We prove that: (a) the LP ...

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