We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the p...
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We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better scaling properties than painvise averaging, an alternative that has received much recent attention. Consensus propagation can be viewed as a special case of belief propagation, and our results contribute to the belief propagation literature. In particular, beyond singly-connected graphs, there are very few classes of relevant problems for which belief propagation is known to converge.
Low-density parity-check codes (LDPC) can have an impressive performance under iterative decoding algorithms. In this paper we introduce a method to construct high coding gain lattices with low decoding complexity bas...
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Low-density parity-check codes (LDPC) can have an impressive performance under iterative decoding algorithms. In this paper we introduce a method to construct high coding gain lattices with low decoding complexity based on LDPC codes. To construct such lattices we apply Construction D', due to Bos, Conway, and Sloane, to a set of parity checks defining a family of nested LDPC codes. For the decoding algorithm, we generalize the application of max-sumalgorithm to the Tanner graph of lattices. Bounds on the decoding complexity are derived and our analysis shows that using LDPC codes results in low decoding complexity for the proposed lattices. The progressive edge growth (PEG) algorithm is then extended to construct a class of nested regular LDPC codes which are in turn used to generate low density parity check lattices. Using this approach, a class of two-level lattices is constructed. The performance of this class improves when the dimension increases and is within 3 dB of the Shannon limit for error probabilities of about 10(-6). This is while the decoding complexity is still quite manageable even for dimensions of a few thousands.
In this paper, we develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low-cost, yet effective, decoding of (high-rate) finite-geome...
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In this paper, we develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low-cost, yet effective, decoding of (high-rate) finite-geometry (FG) LDPC codes. The decoding procedure updates iteratively the hard-decision received vector in search of a valid codeword in the vector space. Only one bit is changed in each iteration, and the bit-selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optional mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for FG-LDPC codes.
We develop and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined-on graphs with cycles. By decomposing the original dis...
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We develop and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined-on graphs with cycles. By decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: a) a tree-related linear program (LP), which is derived from the Lagrangian dual of the upper bounds;and b) a tree-reweighted max-product message-passing algorithm that is related to but distinct from the max-product algorithm. In this way, we establish a connection between a certain LP relaxation of the mode-finding problem and a reweighted form of the max-product (min-sum) message-passing algorithm.
An analogy is examined between serially concatenated codes and parallel concatenations whose interleavers;are described by bipartite graphs with good expanding properties. In particular, a modified expander code const...
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An analogy is examined between serially concatenated codes and parallel concatenations whose interleavers;are described by bipartite graphs with good expanding properties. In particular, a modified expander code construction is shown to behave very much like Forney's classical concatenated codes, though with improved decoding complexity. It is proved that these new codes achieve the Zyablov bound delta(Z) on the minimum distance. For these codes, a soft-decision, reliability-based, linear-time decoding algorithm is introduced, that corrects any fraction of errors up to almost delta(Z)/2. For the binary-symmetric channel, this algorithm's error exponent attains the Forney bound previously known only for classical (serial) concatenations.
An analogy is examined between serially concatenated codes and parallel concatenations whose interleavers;are described by bipartite graphs with good expanding properties. In particular, a modified expander code const...
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ISBN:
(纸本)0780377281
An analogy is examined between serially concatenated codes and parallel concatenations whose interleavers;are described by bipartite graphs with good expanding properties. In particular, a modified expander code construction is shown to behave very much like Forney's classical concatenated codes, though with improved decoding complexity. It is proved that these new codes achieve the Zyablov bound delta(Z) on the minimum distance. For these codes, a soft-decision, reliability-based, linear-time decoding algorithm is introduced, that corrects any fraction of errors up to almost delta(Z)/2. For the binary-symmetric channel, this algorithm's error exponent attains the Forney bound previously known only for classical (serial) concatenations.
This paper investigates two quantization schemes on three soft-output message-passing decoding algorithms for 2-dimensional product codes. Quantization sensitivity on code rates and channel conditions is also investig...
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ISBN:
(纸本)0780382196
This paper investigates two quantization schemes on three soft-output message-passing decoding algorithms for 2-dimensional product codes. Quantization sensitivity on code rates and channel conditions is also investigated. The surprising yet encouraging result is that a simple (3,1) uniform quantization scheme on the min-sum algorithm results in the best overall quality in terms of space, performance and complexity.
In this correspondence we study the decoding problem in an uncertain noise environment. If the receiver knows the noise probability density function (pdf) at each time slot or its a priori probability the standard Vit...
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In this correspondence we study the decoding problem in an uncertain noise environment. If the receiver knows the noise probability density function (pdf) at each time slot or its a priori probability the standard Viterbi algorithm (VA) or the a posteriori probability (APP) algorithm can achieve optimal performance. However, if the actual noise distribution differs From the noise model used to design the receiver, there can be significant performance degradation due to the model mismatch. The minimax concept is used to minimize the worst possible error performance over a family of possible channel noise pdf's. We show that the optimal robust scheme is difficult to derive;therefore, alternative, practically feasible, robust decoding schemes are presented and implemented on VA decoder and two-way APP decoder. Performance analysis and numerical results show our robust decoders have a performance advantage over standard decoders in uncertain noise channels, with no or little computational overhead. Our robust decoding approach can also explain why for turbo decoding overestimating the noise variance gives better results than underestimating it.
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