An enumerative method for runlength-limited codes: permutation codes
نویسندگان
چکیده
Permutation codes, introduced by Slepian, were shown to perform well on an additive white Gaussian noise (AWGN) channel. Unfortunately, these codes required large lookup tables, making them quite complex to implement even though the maximum-likelihood decoder is very simple. In this correspondence, we present an enumeration scheme which encodes and decodes permutation codes with low complexity. We concentrate on the use of permutation codes for constructing high-rate codes that satisfy runlength-limited constraints. Wolf showed that permutation codes can be used for runlength constraints and that they have rate that asymptotically achieves the capacity of a noiseless, runlength-limited constrained channel. Wolf, however, gave no efficient encoders/decoder. Our code construction is enumerative, but unlike other enumerative codes, has storage requirements that are a function of the runlength parameters d and k instead of the block length n. In addition, these codes have error detection and correction capabilities. Finally, we use this approach to construct (0; G=I) codes whereby all odd-numbered occurrences of double-adjacent errors are detected. As an example, a 99.2% efficient, rate 496=528, (0; 6=3) code is presented.
منابع مشابه
On Error Propagation Assessment of High Rate Runlength-Limited Codes
A framework for the analysis of error propagation for high rate runlength-limited codes is developed. The susceptibility to errors of capacity approaching code constructions, the enumerative and sequence replacement technique and bit stuffing, are analyzed in detail. It is shown that the first two techniques experience low error propagation and that they are superior to the popular bit-stuffing...
متن کاملMaximum runlength-limited codes with error control capabilities
New methods are presented to protect maximum runlength-limited sequences against random and burst errors and to avoid error propagation. The methods employ parallel conversion techniques and enumerative coding algorithms that transform binary user information into constrained codewords. The new schemes have a low complexity and are very efficient. The approach can be used for modulation coding ...
متن کاملError Propagation Assessment of Enumerative Coding Schemes Kees
2591 consisting of two four-state trellises. To this point, though, no new codes comparable to, for example, the rate 4=5 and the rate 8=9 MTR codes in [10] for the (1 0 D) (1 + D) 3 and (1 0 D) (1 + D) 4 channels have been found. For future work, an interesting research problem would be to relax the trellis-matching constraint to enlarge the constellations, thus obtaining higher-rate codes. Of...
متن کاملCoding for delay-insensitive communication with partial synchronization
C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379-423, July 1948. P. A. Franaszek, “Sequence-state coding for digital transmission,” Bell Syst. Tech. J., vol. 47, pp. 143-157, Jan. 1968. G. F. M. Beenker and K. A. Schouhamer Immink, “A generalized method for encoding and decoding run-length-limited binary sequences,” IEEE Trans. Inform. Theory, vol. ...
متن کاملEfficient Coding for a Two-Dimensional Runlength-Limited Constraint
Runlength-limited (d, k) constraints and codes are widely used in digital data recording and transmission applications. Generalizations of runlength constraints to two dimensions are of potential interest in page-oriented information storage systems. However, in contrast to the one-dimensional case, little is known about the information-theoretic properties of two-dimensional constraints or the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IEEE Trans. Information Theory
دوره 45 شماره
صفحات -
تاریخ انتشار 1999