Bounded minimum distance decoding of unit memory codes

Dettmar, Uwe; Serger, U.K.

doi:10.1109/18.370160

Cited by 14 publications

(43 citation statements)

References 6 publications

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“…The fourth is a d free = 5 systematic, rate 4/8 UMC that does not have the multiscale structure (referred to as SYST). The generator polynomials for this code are F 0 = [1,2,4,8,6,3,4,12] and F 1 = [0,0,0,0, 9,14,11,7]. Fig.…”

Section: Simulations and Analysismentioning

confidence: 99%

Multiscale unit‐memory convolutional codes

Nagaraj

Bell

2013

IET Communications

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In this study, authors propose structure to unit memory (UM) convolutional codes that greatly simplify their decoding when using sequential or suboptimal L-decoders. The multiscale structure proposed in this study preserves the word-oriented nature of unit memory codes (UMCs), but allows for processing the code in blocks of sizes less than the memory of the code with non-Viterbi-type decoders. At one end of the multiscale structure are generic UMCs. At the other end are structured systematic UMCs that can be decoded with the same ease as conventional multimemory convolutional codes with sequential or L-decoders. As a special case, the authors show quick-look parity check systematic codes of arbitrary rates that are better than previously known optimum minimum distance systematic convolutional codes. These codes are derived from block codes and the convolutional code can be decoded using the syndrome decoder of the underlying block code. The authors present simulation results and analysis to support the proposed multiscale UM convolutional codes.

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Section: Simulations and Analysismentioning

confidence: 99%

Multiscale unit‐memory convolutional codes

Nagaraj

Bell

2013

IET Communications

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“…where d 1 , d 2 , and d α denote the distances of the codes generated by G 1 , G 2 , and [G T 1 , G T 2 ] T respectively. In [20], a decoding algorithm is given, which is guaranteed to be successful if the number of errors does not exceed half the designed extended row distance for any ι, i.e., it decodes successfully if…”

Section: A Convolutional Codesmentioning

confidence: 99%

“…We focus on constructions that result in a convolutional code of memory M = 1, i.e., UM codes. For these codes, the decoder introduced in [20] can efficiently decode up to half the designed extended row distance, by a combination of bounded minimum distance (BMD) decoding in the blocks and trellis-based decoding with the Viterbi algorithm. A key step in this algorithm is decoding blocks in the cosets given by successfully decoded neighboring blocks.…”

Section: Pir With Byzantine Servers and Convolutional Codesmentioning

confidence: 99%

“…The large number of states makes trellis decoding of the convolutional code infeasible. In [20] an algorithm combining BMD decoding in the blocks and Viterbi decoding on a reduced trellis is given, with decoding complexity only cubic in n, if the complexity of the block decoders is quadratic in n. We give a brief description of this algorithm and show how it can be applied to decode the responses.…”

Section: Decodingmentioning

confidence: 99%

“…2) From the blocks successfully decoded in step 1) decode l F steps forward and l B backward (see [20]) in the respective coset C ⋆ (D + E 1 ) or C ⋆ (D + E 2 ). By Lemma 4 these are RS(n, 2k + t − 1) codes and can therefore be decoded up to half their minimum distance d 1 = d 2 = n − 2k − t + 2.…”

Section: Decodingmentioning

confidence: 99%

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Private Streaming with Convolutional Codes

Holzbaur

Freij-Hollanti

Wachter-Zeh

et al. 2018

2018 IEEE Information Theory Workshop (ITW)

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Recently, information-theoretic private information retrieval (PIR) from coded storage systems has gained a lot of attention, and a general star product PIR scheme was proposed. In this paper, the star product scheme is adopted, with appropriate modifications, to the case of private (e.g., video) streaming. It is assumed that the files to be streamed are stored on n servers in a coded form, and the streaming is carried out via a convolutional code. The star product scheme is defined for this special case, and various properties are analyzed for two channel models related to straggling and byzantine servers, both in the baseline case as well as with colluding servers. The achieved PIR rates for the given models are derived and for the first model shown to be asymptotically optimal, when the number of stripes in a file is large. The second scheme introduced in this work is shown to be the equivalent of block convolutional codes in the PIR setting. For the Byzantine server model, it is shown to outperform the trivial scheme of downloading stripes of the desired file separately without memory.

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Interleaving for outer convolutional codes in DS-CDMA systems

Bruck¹,

Sorger

Gligorevic

et al. 2000

IEEE Trans. Commun.

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In DS CDMA systems the probability of error for each user depends on the crosscorrelation between the spreading sequences and on the received energies of all users. Thus even Maximum Likelihood joint detection might in general have a large loss compared to one user transmission. Choosing the individual error correcting codes of all users in a suitable way reduces this loss for given crosscorrelation values. This may be achieved by interleaving the convolutional codes used. It is theoretically shown for a certain kind of interleaving and a moderate codelength that almost the complete in uence of the interuser interference can be eliminated for large signal to noise ratios. Hence the performance of a coded DS CDMA system comes close to transmission without interuser interference. Simulations con rm the analysis.

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Bounded minimum distance decoding of unit memory codes

Cited by 14 publications

References 6 publications

Multiscale unit‐memory convolutional codes

Multiscale unit‐memory convolutional codes

Private Streaming with Convolutional Codes

Interleaving for outer convolutional codes in DS-CDMA systems

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