We study the performance of the maximum likelihood (ML) method in population decoding as a function of the population size. Assuming uncorrelated noise in neural responses, the ML performance, quantified by the expected square difference between the estimated and the actual quantity, follows closely the optimal Cramer-Rao bound, provided that the population size is sufficiently large. However, ...

In many communications problems, maximum-likelihood (ML) decoding reduces to finding the closest (skewed) lattice point in N-dimensions to a given point x E CN. In its full generality, this problem is known to he NP-complete and requires exponential complexity in iV. Recently, the expected complexity of the sphere decoder, a particular algorithm that solves the ML problem exactly, has been comp...

For a class C of binary linear codes, we write θC : (0, 1) → [0, 12 ] for the maximum-likelihood decoding threshold function of C, the function whose value at R ∈ (0, 1) is the largest bit-error rate p that codes in C can tolerate with a negligible probability of maximum-likelihood decoding error across a binary symmetric channel. We show that, if C is the class of cycle codes of graphs, then θ...

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...

Raptor codes have been widely used in many multimedia broadcast/multicast applications. However, our understanding of Raptor codes is still incomplete due to the insufficient amount of theoretical work on the performance analysis of Raptor codes, particularly under maximum-likelihood (ML) decoding, which provides an optimal benchmark on the system performance for the other decoding schemes to c...

The problem of finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In...

A fundamental concept in secure communication of data is the ability to detect and correct errors. In this report, we analyse a sophisticated error detection and correction algorithm when the communication medium consists of written messages tied to the legs of carrier pigeons.

The mutual information between a set of stimuli and the elicited neural responses is compared to the corresponding decoded information. The decoding procedure is presented as an artificial distortion of the joint probabilities between stimuli and responses. The information loss is quantified. Whenever the probabilities are only slightly distorted, the information loss is shown to be quadratic i...

In this work, the priority-first sequential-search decoding algorithm proposed in [8] is revisited. By replacing the conventional Fano metric by one that is derived based on the Wagner rule, the sequentialsearch decoding in [8] guarantees the maximum-likelihood (ML) performance, and hence, was named the maximum-likelihood sequential decoding algorithm (MLSDA). It was then concluded by simulatio...

We consider the reliability-based heuristic search methods for maximum likelihood decoding, which generate test error patterns (or, equivalently, candidate codewords) according to their heuristic values. Some studies have proposed methods for reducing the space complexity of these algorithms, which is crucially large for long block codes at medium to low signal to noise ratios of the channel. I...