John MacLaren Walsh

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—The turbo decoder was not originally introduced as a solution to an optimization problem, which has impeded attempts to explain its excellent performance. Here it is shown, that the turbo decoder is an iterative method seeking a solution to an intuitively pleasing constrained optimization problem. In particular, the turbo decoder seeks the(More)
—A new computational technique is presented for determining rate regions for coded networks. The technique directly manipulates the extreme ray representation of inner and outer bounds for the region of entropic vectors. We use new inner bounds on region of entropic vectors based on conic hull of ranks of representable matroids. In particular, the(More)
—A computational technique for determining rate regions for networks and multilevel diversity coding systems based on inner and outer bounds for the region of entropic vectors is discussed. An inner bound based on binary representable matroids is discussed that has the added benefit of identifying optimal linear codes. The technique is demonstrated on a(More)
—Via multiterminal information theory, a framework is presented for deriving fundamental rate delay tradeoffs that delay mitigating codes must have when utilized over multipath routed and random linear network coded networks. The rate delay tradeoff is formulated as a calculus problem on a capacity region of a related abstracted broadcast channel. Given(More)
—The primary contribution is a finite terminating algorithm that determines membership of a candidate entropy vector in the set of binary entropy vectors Φ N. We outline the relationship between Φ N and its unbounded cardinality discrete random variable counterpart ¯ Γ * N (or its normalization ¯ Ω * N). We discuss connections between Φ N and ¯ Ω * N. For(More)
Many previous attempts at analyzing the convergence behavior of turbo and iterative decoding, such as EXIT style analysis [1] and density evolution [2], ultimately appeal to results which become valid only when the block length grows rather large, while still other attempts, such as connections to factor graphs [3] and belief propagation [4], have been(More)
—Several properties of the inner bound on the region of entropic vectors obtained from representable ma-troids are derived. In particular, it is shown that: I) It suffices to check size 2 minors of an integer-valued vector to determine if it is a valid matroid rank; II) the subset of the extreme rays of the Shannon outer bound (the extremal polymatroids)(More)
— Belief propagation, via a novel reinterpretation of the Bethe free energy's pseudo-dual, is shown to be related to a novel relaxation of maximum likelihood detection via a constrained optimization. The conventional maximum likelihood detection falls out for a zero constraint, and belief propagation's fixed points are obtained for other constraint values.