Constrained coding for binary channels with high intersymbol interference

Abstract

Partial-response (PR) signaling is used to model communications channels with intersymbol interference (ISI) such as the magnetic-recording channel and the copper-wire channel for digital subscriber lines. Coding for improving noise immunity in higher order partial-response channels, such as the "extended" class-4 channels denoted EPR4, E 2 PR4, E 3 PR4, has become an important subject as the linear densities in magnetic recording approach those at which these partial-response channels are the best models of real channels. In this paper, we consider partialresponse channels for which ISI is so severe that the channels fail to achieve the matched-filter bound (MFB) for symbol error rate, assuming maximum-likelihood decoding. We show that their performance can be improved to the MFB by high-rate codes based on constrained systems, some of which may even simplify the Viterbi detectors relative to the uncoded channels. We present several examples of high-rate constrained codes for E 2 PR4 and E 3 PR4 channels and evaluate their performance by simulation.

Reduced complexity sequence detection for high-order partial response channels

“…Bliss [12]-[14], Karabed et al [11] and Knudsen-Fitzpatrick et al [17] introduced at the same time a 8/9 block code that maps eight input bits into nine code bits with time-varying MTR (TMTR) constraints. The major disadvantage of this code is that its restriction on allowed tribits requires an implementation of the Viterbi detector that is variable in time, which significantly increases the detector's complexity and reduces the speed.…”

“…The major disadvantage of this code is that its restriction on allowed tribits requires an implementation of the Viterbi detector that is variable in time, which significantly increases the detector's complexity and reduces the speed. The TMTR block code is constructed by deleting all codewords that contain quadbits and by restricting tribits to certain positions [11]. Because the beginning of the tribit is allowed at positions 2, 4, 6, and 9, with the tribit starting at position 9 being wrapped up in the next word, this implementation results in a time-varying trellis.…”

Time-varying maximum transition run constraints

“…Let . Let denote the polynomial obtained from (6), such that the capacity of TMTR equals the base-logarithm of the largest positive real root of . To show that the largest positive real root of exceeds that of in some interval , we show that for , the largest real root of in , .…”

“…Recently, Moision et al [8] and Karabed et al [6] used error-event analysis on partial-response channels to design codes that forbid the appearance of certain patterns in a periodic manner. The resulting codes successfully eliminated problematic sequences in the data recording or retrieval process, and gave improved code distance and detection performance.…”

Soft-decision decoding of MTR codes over magnetic recording channels

“…Performanse SOVA detektora u velikoj meri su određene ulaznim sekvencama grešaka e x , koje rezultuju malim kvadratnim euklidskim rastojanjem kanala [7] , (43) Na osnovu klasifikacije ulaznih sekvenci grešaka [7] i [82], koje daju malo kvadratno euklidsko rastojanje PR kanala, moguće je identifikovati određene uzorke u ulaznoj sekvenci čijim eliminisanjem bi se u određenoj meri povećalo kvadratno euklidsko rastojanje kanala, pomoću pogodno konstruisanih modulacionih kodova, a samim tim poboljšale performanse detektora [1], [73], [83] i [84].…”