Article

# Coding Techniques for Partial-Response Channels

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## Abstract

A coding technique for improving the reliability of digital transmission over noisy partial-response channels with characteristics (± D <sup>m</sup>), m =1, 2, where the channel input symbols are constrained to be ±1, is presented. In particular, the application of a traditional modulation code as an inner code of a concentrated coding scheme in which the outer code is designed for maximum (free) Hamming distance is considered. A performance comparison is made between the concentrated scheme and a coding technique presented by Wolf and G. Ungerboeck (see ibid., vol. COM-34, p.765-773, Aug. 1986) for the dicode channel with transfer function (1- D )

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... The code-efficiency can be expressed in terms of the code-rate R. The asymptotic coding gain GD is now defined as GD = Rdb(coded) db(uncoded) . This equality indicates the saving in required energy-per-bit to noise-power-density ratio of the coded scheme relative to the uncoded case [44]. ...
Chapter
Baseband modulation codes are widely applied in such diverse fields as digital line transmission [21, 28, 18, 116], digital optical transmission [111, 16], and digital magnetic and optical storage [ 105, 100, 106]. They act to translate the source data sequence d n into a sequence a k that is transmitted across the channel (Fig. 4.1; see also Chapter 3). The principal goal is to enable the receiver to produce reliable decisions $${\hat d_n}$$ about d n . Code design should, therefore, account for the characteristics of both channel and receiver. (Because modulation coding is the only type of coding that we consider in this chapter, we shall usually say ‘coding’ where we mean ‘modulation coding’.)
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Continuous phase modulation-Part 11: Partial response signaling QP, an improved code for high density digital recording
• T Aulin
• N Rydbeck
• C E Sundberg
T. Aulin, N. Rydbeck, and C. E. Sundberg, " Continuous phase modulation-Part 11: Partial response signaling, " ZEEE Truns. Corn-mun., vol. COM-29, pp. 210-225, Mar. 1981. J. A. Bixby and R. A. Ketcham, " QP, an improved code for high density digital recording, " IEEE Trans. Magn., vol. MAG-15, pp. pp. 1557-1569, NOV. 1986. 1465-1467, NOV. 1979.