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59
LowDensity ParityCheck Codes
, 1963
"... Preface The Noisy Channel Coding Theorem discovered by C. E. Shannon in 1948 offered communication engineers the possibility of reducing error rates on noisy channels to negligible levels without sacrificing data rates. The primary obstacle to the practical use of this theorem has been the equipment ..."
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Cited by 894 (1 self)
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Preface The Noisy Channel Coding Theorem discovered by C. E. Shannon in 1948 offered communication engineers the possibility of reducing error rates on noisy channels to negligible levels without sacrificing data rates. The primary obstacle to the practical use of this theorem has been the equipment complexity and the computation time required to decode the noisy received data.
Applications of ErrorControl Coding
, 1998
"... An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video t ..."
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Cited by 165 (0 self)
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An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video transmission. Examples, both historical and current, are given that typify the different approaches used in each application area. Although no attempt is made to be comprehensive in our coverage, the examples chosen clearly illustrate the richness, variety, and importance of errorcontrol coding methods in modern digital applications.
A unified framework for tree search decoding: rediscovering the sequential decoder
 IEEE Trans. Inform. Theory
, 2006
"... Abstract—We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopte ..."
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Cited by 51 (2 self)
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Abstract—We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopted. In our framework, the CLPS algorithm is decomposed into the preprocessing and tree search stages. The role of the preprocessing stage is to expose the tree structure in a form matched to the search stage. We argue that the forward and feedback (matrix) filters of the minimum meansquare error decision feedback equalizer (MMSEDFE) are instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSEDFE filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity, at the expense of a marginal performance loss. For the search stage, we present a generic method, based on the branch and bound (BB) algorithm, and show that it encompasses all existing sphere decoders as special cases. The proposed generic algorithm further allows for an interesting classification of tree search decoders, sheds more light on the structural properties of all known sphere decoders, and inspires the design of more efficient decoders. In particular, an efficient decoding algorithm that resembles the wellknown Fano sequential decoder is identified. The excellent performance–complexity tradeoff achieved by the proposed MMSEDFE Fano decoder is established via simulation results and analytical arguments in several multipleinput multipleoutput (MIMO) and intersymbol interference (ISI) scenarios. Index Terms—Closest lattice point search (CLPS), Fano decoder, lattice codes, sequential decoding, sphere decoding, tree search. I.
Coding for Interactive Communication
 IN PROCEEDINGS OF THE 25TH ANNUAL SYMPOSIUM ON THEORY OF COMPUTING
, 1996
"... Let the input to a computation problem be split between two processors connected by a communication link; and let an interactive protocol ß be known by which, on any input, the processors can solve the problem using no more than T transmissions of bits between them, provided the channel is noiseless ..."
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Cited by 38 (4 self)
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Let the input to a computation problem be split between two processors connected by a communication link; and let an interactive protocol ß be known by which, on any input, the processors can solve the problem using no more than T transmissions of bits between them, provided the channel is noiseless in each direction. We study the following question: if in fact the channel is noisy, what is the effect upon the number of transmissions needed in order to solve the computation problem reliably? Technologically this concern is motivated by the increasing importance of communication as a resource in computing, and by the tradeoff in communications equipment between bandwidth, reliability and expense. We treat a model with random channel noise. We describe a deterministic method for simulating noiselesschannel protocols on noisy channels, with only a constant slowdown. This is an analog for general interactive protocols of Shannon's coding theorem, which deals only with data transmission, ...
Algorithmic Complexity in Coding Theory and the Minimum Distance Problem
, 1997
"... We start with an overview of algorithmiccomplexity problems in coding theory We then show that the problem of computing the minimum distance of a binary linear code is NPhard, and the corresponding decision problem is NPcomplete. This constitutes a proof of the conjecture Bedekamp, McEliece, van T ..."
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Cited by 34 (2 self)
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We start with an overview of algorithmiccomplexity problems in coding theory We then show that the problem of computing the minimum distance of a binary linear code is NPhard, and the corresponding decision problem is NPcomplete. This constitutes a proof of the conjecture Bedekamp, McEliece, van Tilborg, dating back to 1978. Extensions and applications of this result to other problems in coding theory are discussed.
Feedback and error protection strategies for wireless progressive video transmission
 IEEE Transactions on Circuits and Systems for Video Technology
, 2002
"... Abstract—In this work, feedback and errorprotection strategies for wireless progressive video transmission are presented and evaluated. Simple but meaningful models for a mobile radio channel are introduced, and a channelcoding system based on highmemory ratecompatible punctured convolutional co ..."
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Cited by 14 (3 self)
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Abstract—In this work, feedback and errorprotection strategies for wireless progressive video transmission are presented and evaluated. Simple but meaningful models for a mobile radio channel are introduced, and a channelcoding system based on highmemory ratecompatible punctured convolutional codes with an appropriate sequential decoding algorithm, the farend error decoder (FEED), are presented. Furthermore, in combination with puncturing, we devise a method for unequal error protection (UEP) and error localization within a progressively coded source message without any additional error detection code. In a change of paradigm, the FEEDbased channelcoding system does not aim to minimize the bit or word error probability, but to delay the first error within a data frame as far as possible. In addition, this channelcoding scheme and the FEED algorithm can be used efficiently in an Automatic Repeat reQuest (ARQ) environment. We present different ARQ strategies. For all forward errorcorrection schemes bounds are specified which allow the estimation of the performance and appropriate rate allocation. Additionally, we briefly discuss an efficient fine granular scalable video compression scheme, the progressive texture video codec (PTVC). The proposed scheme generates an embedded bitstream for each frame and allows to adjust the reference frames. These source and channelcoding algorithms are used to design several video communication systems based on forward errorcorrection and ARQ methods. The resulting systems are presented and compared. Performance estimations based on bounding techniques and optimized rateallocation algorithms are derived and applied. Experimental results show the extraordinary improvement potential of the proposed systems compared to standard schemes. Video communication over very low bitrate mobile channels with varying channel conditions is thus made possible. Index Terms—Feedbackbased video transmission, H.26L, progressive/scalable video coding, ratedistortion optimization, unequal error protection, wireless video transmission. I.
Huffman Tree Based Metric Derivation for a Lowcomplexity Sequential Soft VLC Decoding
 in Proceedings of ICC'02
, 2002
"... This paper considers VLC decoding algorithms based on MAP sequence estimation techniques, using residual source redundancy to provide channel error correction. These algorithms rely on soft values available at the entrance of the VLC decoder. We present here a new soft VLC decoding algorithm based o ..."
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Cited by 14 (4 self)
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This paper considers VLC decoding algorithms based on MAP sequence estimation techniques, using residual source redundancy to provide channel error correction. These algorithms rely on soft values available at the entrance of the VLC decoder. We present here a new soft VLC decoding algorithm based on a sequential decoding technique that is very efficient in terms of decoding complexity.
Progressive Source Coding Combined with Regressive Channel Coding on Varying Channels
 in Proc. 3rd ITG Conf. Source and Channel Coding
, 2000
"...  A channel coding system for strongly varying channels (mobile radio, Internet) unknown to the encoder is presented. It matches progressively coded sources (e.g., video, images, audio, speech) with convolutional codes of very high memory applying regressive redundancy over the data frame of the sou ..."
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Cited by 13 (6 self)
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 A channel coding system for strongly varying channels (mobile radio, Internet) unknown to the encoder is presented. It matches progressively coded sources (e.g., video, images, audio, speech) with convolutional codes of very high memory applying regressive redundancy over the data frame of the source. The channel decoder with scalable complexity and delay employs modified sequential decoding. The decoder uses a new algorithm, the 'far end error decoder (FEED)' which in a change of paradigm does not aim at low error rate, but rather makes the first error as far out as possible under the actual channel conditions. We determine the errorfree region of the frame which means that for progressively coded sources we achieve the best reconstruction quality possible. The decoding method is selfadaptive to varying and unknown channel conditions (interference, fading, packet loss) and provides graceful degradation. Results with SPIHT coded images show performances better than previous known FEC schemes. Potentials for further improvements of this scheme are discussed.
Channel Coding: The Road to Channel Capacity
, 2006
"... Submitted to the Proceedings of the IEEE ..."
DeepSpace Communications and Coding: A Marriage Made in Heaven
 in Proceedings of the 1992 DLR Seminar "Advanced Methods for Satellite and Deep Space Comm
, 1992
"... this paper we have followed the usual communications practice of not distinguishing between a "code" (i. e., the set of all codewords) and an "encoder," but this difference can be important in coding theory.] The LinLyne code had a memory of M = 20, i. e., the encoder remembered twenty past informa ..."
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Cited by 9 (3 self)
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this paper we have followed the usual communications practice of not distinguishing between a "code" (i. e., the set of all codewords) and an "encoder," but this difference can be important in coding theory.] The LinLyne code had a memory of M = 20, i. e., the encoder remembered twenty past information bits as well as the current information bit when forming the two encoded binary digits that are emitted for each input information bit. It was known that the minimum Hamming distance dmin of this code was 11. This is the minimum distance between two encoded sequences of length 2 (M+1) = 22 digits (one "constraint length") that correspond to different values of the initial information bit. If one uses these code parameters mindlessly in (17), one computes an estimated coding gain of G c 5 (7.0 dB), but this estimate is so optimistic that it must be taken with a grain of salt! [In fact, one should really use in (17) the free distance, d free , of the convolutional code, which is the minimum Hamming distance between two encoded sequences of infinite length that correspond to different values of the initial information bit. This would, of course, give an even more optimistic estimate of G c. !] The problem is not one of great multiplicity of near neighbors as it was for the ReedMuller code. Rather, the problem is that one must take into account the fact that although Fanoalgorithm sequential decoding is virtually maximumlikelihood decoding if the decoder is allowed to compute until it makes a decoding decision, in practice one always aborts the decoding after some predetermined amount of computation on a frame and announces erasure of the corresponding frame of data. The actual error probability in the nonerased frames is virtually zero since the frames that would have ...