Article

Construction of Capacity Achieving (M, d, infty) Constrained Codes With Least Decoder Window Length

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Abstract

We present capacity achieving multilevel run-length-limited (ML-RLL) codes that can be decoded by a sliding window of size $2$ .

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The existence of 100% efficient (i.e., capacity-achieving) fixed-rate codes for input-constrained, noiseless channels is guaranteed provided the channel has rational capacity. A class of M-ary runlength-limited (M,d,∞) constraints was shown in previous work to have rational capacity. In this correspondence we present a code construction procedure for obtaining 100% efficient codes with the fewest number of encoder states for all (M,d,∞) constraints with rational capacity. The decoders are sliding-block decoders with sliding window size d+1
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Presents two results on the Shannon capacity of M-ary (d,k) codes. First the authors show that 100% efficient fixed-rate codes are impossible for all values of (M,d,k), 0&les;d<k<∞, M<∞, thereby extending a result of Ashley and Siegel (1987) to M-ary channels. Second, they show that for k=∞, there exist an infinite number of 100% efficient M-ary (d,k) codes, and they construct three such capacity-achieving codes
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The capacity region of frame-synchronous and frame-asynchronous, discrete, two-user multiple-access channels with finite memory is obtained. Frame synchronism refers to the ability of the transmitters to send their code words in unison. The absence of frame synchronism in memoryless multiple-access channels is known to result in the removal of the convex hull operation from the expression of the capacity region. It is shown that when the channel has memory, frame asynchronism rules out nonstationary inputs to achieve any point in the capacity region, thereby allowing only coding strategies that involve cooperation in the frequency domain but not in the time domain. This restriction drastically reduces the capacity region of some multiple-access channels with memory, and in particular the total capacity of the channel, which is invariant to frame asynchronism for memoryless channels
The scientific responsibility rests with its authors
  • Leuven
Leuven, project OT/05/40 (Large rank structured matrix computations), CoE EF/05/006 Optimization in Engineering (OPTEC), by the Fund for Scientific Research–Flanders (Belgium), G.0423.05 (RAM: Rational modeling: optimal conditioning and stable algorithms), and by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office, Belgian Network DYSCO (Dynamical Systems, Control, and Optimization). The scientific responsibility rests with its authors.
Germany (e-mail: immink@exp-math.uni-esen.de)
  • Essen
Essen, Germany (e-mail: immink@exp-math.uni-esen.de).