Signal-space characterization of iterative decoding

  title={Signal-space characterization of iterative decoding},
  author={Brendan J. Frey and Ralf Koetter and Alexander Vardy},
  journal={IEEE Trans. Inf. Theory},
By tracing the flow of computations in the iterative decoders for low-density parity-check codes, we formulate a signal-space view for a finite number of iterations in a finite-length code. On a Gaussian channel, maximum a posteriori (MAP) codeword decoding (or "maximum-likelihood decoding") decodes to the codeword signal that is closest to the channel output in Euclidean distance. In contrast, we show that iterative decoding decodes to the "pseudosignal" that has highest correlation with the… 
Graph-Cover Decoding and Finite-Length Analysis of Message-Passing Iterative Decoding of LDPC Codes
The goal of the present paper is the derivation of a framework for the finite-length analysis of message-passing iterative decoding of low-density parity-check codes and introduces the concept of graph-cover decoding, a theoretical tool that can be used to show connections between linear programming decoding and message- passing iterative decode.
Performance of the Sum-Product Decoding Algorithm on Factor Graphs With Short Cycles
It has been postulated that different factor graph representations of the same parity check code result in different algorithm performance, and it is shown that this is indeed true, and some explanation is offered, and a few researchers' work on factor graph analysis is reviewed.
Graph-covers and iterative decoding of nite length codes
A simple characterization of pseudocodewords from finite covers is given and it is shown that, for the additive, white Gaussian noise channel, their impact is captured in a finite set of “minimal” pseudo-codewords.
Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels
An analysis under the iterative decoding of coset low-density parity-check codes over GF(q), designed for use over arbitrary discrete-memoryless channels, shows that under a Gaussian approximation, the entire q-1-dimensional distribution of the vector messages is described by a single scalar parameter.
Using linear programming to Decode Binary linear codes
The definition of a pseudocodeword unifies other such notions known for iterative algorithms, including "stopping sets," "irreducible closed walks," "trellis cycles," "deviation sets," and "graph covers," which is a lower bound on the classical distance.
Quantized Iterative Message Passing Decoders with Low Error Floor for LDPC Codes
This work shows that a contributor to the error floors observed in the literature may be the imprecise implementation of decoding algorithms and, in particular, the message quantization rules used, and proposes a new quantization method - (q+1)-bit quasi-uniform quantization - that efficiently increases the dynamic range of messages, thereby overcoming a limitation of conventional quantization schemes.
Decomposition Methods for Large Scale LP Decoding
This paper draws on decomposition methods from optimization theory, specifically the alternating direction method of multipliers (ADMM), to develop efficient distributed algorithms for LP decoding, and develops an efficient algorithm for Euclidean norm projection onto the parity polytope.
Low complexity iterative algorithms in channel coding and compressed sensing
This thesis proposes a methodology for selection that relies on the knowledge of potentially harmful topologies that could be present in a code, using the concept of noisy trapping set, for selection of particularly good FAIDs for columnweight-three codes over the Binary Symmetric channel (BSC).
On Pseudocodewords and Decision Regions of Linear Programming Decoding of HDPC Codes
The decision regions of Linear Programming (LP) decoding are explored, and global optimization is presented as a method for finding the minimal pseudoweight of a given code as well as the number of minimal-weight generators.
Code representation and performance of graph-Based decoding
Stopping redundancy measures the complexity requirement for MPID of a redundant graph representation to achieve performance comparable to ML decoding to provide partial confirmation of Schwartz and Vardy conjecture that the stopping redundancy of an MDS code should only depend on its length and minimum distance.


Iterative decoding of binary block and convolutional codes
Using log-likelihood algebra, it is shown that any decoder can be used which accepts soft inputs-including a priori values-and delivers soft outputs that can be split into three terms: the soft channel and aPriori inputs, and the extrinsic value.
Skewness and pseudocodewords in iterative decoding
  • B. Frey, R. Kotter, A. Vardy
  • Computer Science
    Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252)
  • 1998
The authors discuss here how iterative decoding maximizes correlation, and skewness and pseudocodewords in the decoding tree.
Separable MAP "filters" for the decoding of product and concatenated codes
The decoding of multidimensional product codes, using separable symbol-by-symbol maximum a posteriori filters, and the extension of the concept to concatenated convolutional codes is given and some simulation results are presented.
Near optimum error correcting coding and decoding: turbo-codes
A new family of convolutional codes, nicknamed turbo-codes, built from a particular concatenation of two recursive systematic codes, linked together by nonuniform interleaving appears to be close to the theoretical limit predicted by Shannon.
Iterative Decoding of Compound Codes by Probability Propagation in Graphical Models
It is pointed out that iterative decoding algorithms for various codes, including "turbo decoding" of parallel-concatenated convolutional codes, may be viewed as probability propagation in a graphical model of the code.
A recursive approach to low complexity codes
It is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst-error correction abilities.
Channel coding with multilevel/phase signals
A coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. This is achieved by channel coding with expanded
Codes and Decoding on General Graphs
It is showed that many iterative decoding algorithms are special cases of two generic algorithms, the min-sum and sum-product algorithms, which also include non-iterative algorithms such as Viterbi decoding.
Low-density parity-check codes
A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Coding theorems for 'turbo-like' codes
This paper offers a general conjecture about the behavior of the ensemble (maximum-likelihood decoder) word error probability as the word length approches infinity and proves the first rigorous proof of a coding theorem for turbo-like codes.