Upper bounds on the MAP threshold of iterative decoding systems with erasure noise

2012 IEEE International Conference on Communications (ICC)

et al. 2012

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Recently, it has been observed that terminated low-density-parity-check (LDPC) convolutional codes (or spatially-coupled codes) appear to approach capacity universally across the class of binary memoryless channels. This is facilitated by the "threshold saturation" effect whereby the belief-propagation (BP) threshold of the spatially-coupled ensemble is boosted to the maximum a-posteriori (MAP) threshold of the underlying constituent ensemble.In this paper, we consider the universality of spatially-coupled codes over intersymbol-interference (ISI) channels under joint iterative decoding. More specifically, we empirically show that threshold saturation also occurs for the considered problem. This can be observed by first identifying the EXIT curve for erasure noise and the GEXIT curve for general noise that naturally obey the general area theorem. From these curves, the corresponding MAP and the BP thresholds are then numerically obtained.With the fact that regular LDPC codes can achieve the symmetric information rate (SIR) under MAP decoding, spatially-coupled codes with joint iterative decoding can universally approach the SIR of ISI channels. For the dicode erasure channel, Kudekar and Kasai recently reported very similar results based on EXIT-like curves.

“…For simplicity of notation, we drop S 0 in all the expressions although the dependency on S 0 is always implied. From (26) and (27), it is clear that…”

Section: A Gexit Curves For the Isi Channelsmentioning

confidence: 99%

“…where x is the DE FP at channel erasure rate and y = y(x). The formula (14) for the DEC case is equivalent to the result shown in [26] by analyzing the BCJR algorithm.…”

Section: A Bp and Ebp Curves For The Gecmentioning

confidence: 99%

See 1 more Smart Citation

Threshold saturation of spatially-coupled codes on intersymbol-interference channels

Nguyen

Yedla

2012 IEEE International Conference on Communications (ICC)

et al. 2012

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“…Similar to single user channels, the area theorem for the joint decoder can be used to compute an upper bound on the MAP threshold of the joint decoder. For example, this technique was applied to the joint decoding of a finite-state channel and an LDPC code in [12]. It has been observed that this upper bound is tight for regular LDPC ensembles transmitted over the BEC [13].…”

Section: Density Evolution and (G)exit Curvesmentioning

confidence: 99%

Universality for the noisy Slepian-Wolf problem via spatial coupling

Yedla

2011 IEEE International Symposium on Information Theory Proceedings

Narayanan

2011

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Abstract-We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded and transmitted over two independent binary memoryless symmetric channels. Each channel capacity is assumed to be characterized by a single parameter which is not known at the transmitter. The receiver has knowledge of both the source correlation and the channel parameters. We call a system universal if it retains near-capacity performance without channel knowledge at the transmitter.Kudekar et al. recently showed that terminated low-density parity-check (LDPC) convolutional codes (a.k.a. spatially-coupled LDPC ensembles) can have belief-propagation thresholds that approach their maximum a-posteriori thresholds. This was proven for binary erasure channels and shown empirically for binary memoryless symmetric channels. They also conjectured that the principle of spatial coupling is very general and the phenomenon of threshold saturation applies to a very broad class of graphical models. In this work, we derive an area theorem for the joint decoder and empirically show that threshold saturation occurs for this problem. As a result, we demonstrate near-universal performance for this problem using the proposed spatiallycoupled coding system. A similar result is also discussed briefly for the 2-user multiple-access channel.

“…It is also demonstrated that the upper bound can be used to derive new capacity results, such as the dicode erasure channel (DEC). The DEC is a quantized version of the known dicode channel with additive white Gaussian noise (AWGN), which was studied in [13], [14]. DP-based simulations for this channel show that the optimal policy only visits a small (i.e., finite) subset of the state space and the actions associated with those states are unconstrained.…”

Section: Introductionmentioning

confidence: 99%

A Single-Letter Upper Bound on the Feedback Capacity of Unifilar Finite-State Channels

Sabag

Permuter

IEEE Trans. Inform. Theory

2017

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An upper bound on the feedback capacity of unifilar finite-state channels (FSCs) is derived. A new technique, called the Q-contexts, is based on a construction of a directed graph that is used to quantize recursively the receiver's output sequences to a finite set of contexts. For any choice of Q-graph, the feedback capacity is bounded by a singleletter expression, Cfb ≤ sup I(X, S; Y |Q), where the supremum is over P X|S,Q and the distribution of (S, Q) is their stationary distribution. It is shown that the bound is tight for all unifilar FSCs where feedback capacity is known: channels where the state is a function of the outputs, the trapdoor channel, Ising channels, the no-consecutive-ones input-constrained erasure channel and for the memoryless channel. Its efficiency is also demonstrated by deriving a new capacity result for the dicode erasure channel (DEC); the upper bound is obtained directly from the above expression and its tightness is concluded with a general sufficient condition on the optimality of the upper bound. This sufficient condition is based on a fixed point principle of the BCJR equation and, indeed, formulated as a simple lower bound on feedback capacity of unifilar FSCs for arbitrary Q-graphs. This upper bound indicates that a single-letter expression might exist for the capacity of finite-state channels with or without feedback based on a construction of auxiliary random variable with specified structure, such as Q-graph, and not with i.i.d distribution. The upper bound also serves as a non-trivial bound on the capacity of channels without feedback, a problem that is still open. Index TermsConverse, dicode erasure channel, feedback capacity, finite state channels, trapdoor channel, unifilar channels, upper bound.