Topic
List decoding
About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.
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TL;DR: A new algorithm for erasurefree sequential decoding of convolutional codes is introduced which achieves low error probabilities at substantially higher decoding speeds than the Viterbi decoding algorithm.
Abstract: A new algorithm for erasurefree sequential decoding of convolutional codes is introduced which achieves low error probabilities at substantially higher decoding speeds than the Viterbi decoding algorithm. The algorithmic properties of the Multiple Stack Algorithm (MSA) are investigated and it is demonstrated that the MSA reaches a decision with an exponentially rather than Pareto distributed computational effort. The MSA's error probability on the binary symmetric channel is studied as a function of its parameters and its performance and complexity compared to that of the Viterbi algorithm. The MSA is seen to achieve equal and lower error probabilities with a significantly lower average decoding effort. The new algorithm can thus be considered an attractive alternative to the Viterbi algorithm where low error probabilities and high decoding speeds are required simultaneously.
47 citations
TL;DR: The bootstrap step is applied to the weighted bit-flipping algorithm to decode a number of LDPC codes and large improvements in both performance and complexity are observed.
Abstract: An initial bootstrap step for the decoding of low-density parity-check (LDPC) codes is proposed. Decoding is initiated by first erasing a number of less reliable bits. New values and reliabilities are then assigned to erasure bits by passing messages from nonerasure bits through the reliable check equations. The bootstrap step is applied to the weighted bit-flipping algorithm to decode a number of LDPC codes. Large improvements in both performance and complexity are observed.
47 citations
07 Jul 2003
TL;DR: It is proved that deterministic schemes, which guarantee correct recovery of the message, provide no savings and essentially the entire message has to be sent as side information and randomized schemes only need side information of length logarithmic in the message length.
Abstract: Under list decoding of error-correcting codes, the decoding algorithm is allowed to output a small list of codewords that are close to the noisy received word. This relaxation permits recovery even under very high noise thresholds. We consider one possible scenario that would permit disambiguating between the elements of the list, namely where the sender of the message provides some hopefully small amount of side information about the transmitted message on a separate auxiliary channel that is noise-free. This setting becomes meaningful and useful when the amount of side information that needs to be communicated is much smaller than the length of the message. We study what kind of side information is necessary and sufficient in the above context. The short, conceptual answer is that the side information must be randomized and the message recovery is with a small failure probability. Specifically, we prove that deterministic schemes, which guarantee correct recovery of the message, provide no savings and essentially the entire message has to be sent as side information. However there exist randomized schemes, which only need side information of length logarithmic in the message length. In fact, in the limit of repeated communication of several messages, amortized amount of side information needed per message can be a constant independent of the message length or the failure probability. Concretely, we can correct up to a fraction (1/2-/spl gamma/) of errors for binary codes using only 2log(1//spl gamma/)+O(1) amortized bits of side information per message, and this is in fact the best possible (up to additive constant terms).
47 citations
28 Jun 2009
TL;DR: A new compressive sensing scheme, based on codes of graphs, that allows for joint design of sensing matrices and low complexity reconstruction algorithms and for more elaborate greedy reconstruction schemes is proposed.
Abstract: We propose a new compressive sensing scheme, based on codes of graphs, that allows for joint design of sensing matrices and low complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with OMP methods. For more elaborate greedy reconstruction schemes, we propose a new family of list decoding and multiple-basis belief propagation algorithms. Our simulation results indicate that the proposed CS scheme offers good complexity-performance tradeoffs for several classes of sparse signals.
47 citations
TL;DR: This letter proposes a new method to reduce the decoding complexity of ADMM-based LP decoder by decreasing the number of Euclidean projections, and results show that the proposed decoder can still save roughly 20% decoding time even if both the over-relaxation and early termination techniques are used.
Abstract: The Euclidean projection onto check polytopes is the most time-consuming operation in the linear programming (LP) decoding based on alternating direction method of multipliers (ADMM) for low-density parity-check (LDPC) codes. In this letter, instead of reducing the complexity of Euclidean projection itself, we propose a new method to reduce the decoding complexity of ADMM-based LP decoder by decreasing the number of Euclidean projections. In particular, if all absolute values of the element-wise differences between the input vector of Euclidean projection in the current iteration and that in the previous iteration are less than a predefined value, then the Euclidean projection at the current iteration will be no longer performed. Simulation results show that the proposed decoder can still save roughly 20% decoding time even if both the over-relaxation and early termination techniques are used.
47 citations