Discriminated Belief Propagation

Near optimal decoding of good error control codes is generally a difficult task. However, for a certain type of (sufficiently) good codes an efficient decoding algorithm with near optimal performance exists. These codes are defined via a combination of constituent codes with low complexity trellis representations. Their decoding algorithm is an instance of (loopy) belief propagation and is based on an iterative transfer of constituent beliefs. The beliefs are thereby given by the symbol probabilities computed in the constituent trellises. Even though weak constituent codes are employed close to optimal performance is obtained, i.e., the encoder/decoder pair (almost) achieves the information theoretic capacity. However, (loopy) belief propagation only performs well for a rather specific set of codes, which limits its applicability. In this paper a generalisation of iterative decoding is presented. It is proposed to transfer more values than just the constituent beliefs. This is achieved by the transfer of beliefs obtained by independently investigating parts of the code space. This leads to the concept of discriminators, which are used to improve the decoder resolution within certain areas and defines discriminated symbol beliefs. It is shown that these beliefs approximate the overall symbol probabilities. This leads to an iteration rule that (below channel capacity) typically only admits the solution of the overall decoding problem. Via a Gauss approximation a low complexity version of this algorithm is derived. Moreover, the approach may then be applied to a wide range of channel maps without significant complexity increase

some notes on discount factor restrictions for dynamic optimization problems

We consider dynamic optimization problems on one-dimensional state spaces. Un- der standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system xt+1 = h(xt) on the other hand. The purpose of this paper is to survey some of the most important contributions of this literature and to modify or improve them in various directions. We deal in particular with the topological entropy of the dynamical system, with its Lyapunov exponents, and with its periodic orbits.

Inflation Forecast Targeting in an Overlapping Generations Model

In the framework of a standard overlapping generations model, it is shown that active inflation forecast targeting reinforces mechanisms that lead to indeterminacy of the monetary steady state and to countercyclical behavior of young-age consumption. The inflation forecast targeting rule which minimizes the volatility of inflation can be active or passive, depending on the characteristics of shocks and the risk aversion of households. Inflation forecast errors are always greater under active inflation forecast targeting than under passive inflation forecast targeting or strict money growth targeting. The monetary steady state is more likely to be indeterminate under an active rule of inflation forecast targeting than under the corresponding backward-looking rule (inflation targeting), but backward-looking rules can render the monetary steady state unstable.Monetary policy, Inflation forecast targeting, Overlapping generations model

Time-consistent Monetary Policy Rules

A monetary policy rule is a function mapping any given output level of the economy to a corresponding rate of inflation. Such a rule is time-consistent if the central bank has no incentive to deviate from it. Within a simple dynamic model combining an output-inflation trade-off with rational private-sector expectations we study existence and properties of time-consistent monetary policy rules. It is shown that such rules exist only if (i) the central bank gives relatively high weight to price stability and relatively low weight to output stabilization and if (ii) the random shocks to the economy are not too strong. If time-consistent monetary policy rules exist, they are generically non-unique.Monetary policy, Time-consistency, Policy rules, Inflation

On the monodromy of the Hitchin connection

For any genus g > 1 we give an example of a family of smooth complex projective curves of genus g such that the image of the monodromy representation of the Hitchin connection on the sheaf of generalized SL(2)-theta functions of level l different from 1,2,4 and 8 contains an element of infinite order.Comment: 20 pages, revised versio

A dynamic pricipal-agent problem as a feedback Stackelberg differentioal game

We consider situations in which a principal tries to induce an agent to spend e®ort on accumulating a state variable that a®ects the well-being of both parties. The only incentive mechanism that the principal can use is a state-dependent transfer of her own utility to the agent. Formally, the model is a Stackelberg di®erential game in which the players use feedback strategies. Whereas in general Stackelberg di®erential games with feedback strategy spaces the leader's optimization problem has non-standard features that make it extremely hard to solve, in the present case this problem can be rewritten as a standard optimal control problem. Two examples are used to illustrate our approach.