A Leech lattice modem

Lang, G. R.; Longstaff, F.M.

doi:10.1109/49.29618

Cited by 80 publications

(51 citation statements)

References 7 publications

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“…Advanced line probing, adaptive equalization, and precoding techniques are used to increase the signaling rates to as high as 3429 symbols/s, compared to the previous standard of 2400 symbols/s. (In V.34, the data rates are not necessarily integer multiples of the symbol rates, since the signal mapping technique, called shell mapping [42], allows the mapping of fractional bits per symbol.) The V.34 standard also includes two other codes which offer slightly better performance at a cost of increased complexity [41].…”

Section: Applications To Data Transmissionmentioning

confidence: 99%

Applications of ErrorControl Coding

VerdÂ¹,

McLaughlin²

2009

Information Theory

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Abstract-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 error-control coding methods in modern digital applications.

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Section: Applications To Data Transmissionmentioning

confidence: 99%

Applications of ErrorControl Coding

VerdÂ¹,

McLaughlin²

2009

Information Theory

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“…Lang proposed an E 8 lattice code for telephone-line modems to a CCITT international standards committee in the mid-70s, and actually built a Leech lattice modem in the late 1980s [74].…”

Section: B Spherical Lattice Codesmentioning

confidence: 99%

Channel coding: The road to channel capacity

2007

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Starting from Shannon's celebrated 1948 channel coding theorem, we trace the evolution of channel coding from Hamming codes to capacity-approaching codes. We focus on the contributions that have led to the most significant improvements in performance vs. complexity for practical applications, particularly on the additive white Gaussian noise (AWGN) channel. We discuss algebraic block codes, and why they did not prove to be the way to get to the Shannon limit. We trace the antecedents of today's capacity-approaching codes: convolutional codes, concatenated codes, and other probabilistic coding schemes. Finally, we sketch some of the practical applications of these codes.

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“…For example, for 2-D subconstellations composed of 256 points in an N = 32-D space, a direct addressing scheme using a lookup [8] use an addressing scheme which is based on decomposing the space into lower-dimensional subspaces via generating function techniques. Prior to [a], a similar addressing scheme was used by Fischer in [9].…”

Section: 'This Work Was Supported By Natural Sciences and Engineeringmentioning

confidence: 99%

“…This results in an addressing decomposition scheme which has some similarities with the scheme of [8]. More recently, Kschischang in [18] discusses the structure of a prefix code which closely approximates the optimum nonuniform probabilities of the 2-D points.…”

Section: 'This Work Was Supported By Natural Sciences and Engineeringmentioning

confidence: 99%

Efficient, nearly optimum addressing schemes based on partitioning the constellation into the union of blocks

Khandani

Kabal

Proceedings of ICC '93 - IEEE International Conference on Communications

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'Abstract: In this paper, we introduce two efficient addressing schemes for the nearly optimum shaping of multi-dimensional signal spaces. Using K concentric circles, the 2-D (two-dimensional) subspaces are partitioned into K shells of equal volume. is to find a one-to-one mapping between the set of these n-tuples and the set of the integers (0, T -1 1 such that the mapping and its inverse can be easily implemented. In the proposed schemes, the N-D clusters are grouped into blocks such that the addressing within the blocks, which is achieved using a common algorithm for all the blocks, has a low complexity. The addressing of the blocks is based on some recursive relationship which allows us to decompose the problem into smaller parts each of a low complexity. The overall scheme requires a moderate amount of memory and has a small computational complexity. The introduced methods are compared with the previously known schemes. The reduction in the complexity is substantial.

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A Leech lattice modem

Cited by 80 publications

References 7 publications

Applications of ErrorControl Coding

Applications of ErrorControl Coding

Channel coding: The road to channel capacity

Efficient, nearly optimum addressing schemes based on partitioning the constellation into the union of blocks

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