Browsing by Subject "Cutoff rate"

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    Application of guessing to sequential decoding of polarization-adjusted convolutional (PAC) codes
    (Institute of Electrical and Electronics Engineers Inc., 2023-08-16) Moradi, Mohsen
    Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the cutoff rate denotes the region between rates whose average computational complexity of decoding is finite and those which is infinite. In this paper, by benefiting from the polarization and guessing techniques, we prove that the required computation in sequential decoding of pre-transformed polar codes polarizes, and this polarization determines which set of bit positions within the rate profile may result in high computational complexity. Based on this, we propose a technique for taming the Reed-Muller (RM) rate-profile construction, and the performance results demonstrate that the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed RM rate-profile construction and requires a significantly lower computational complexity than the RM rate-profile construction.
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    Channel combining and splitting for cutoff rate improvement
    (Institute of Electrical and Electronics Engineers, 2006) Arikan, E.
    The cutoff rate R0(W) of a discrete memoryless channel (DMC) W is often used as a figure of merit alongside the channel capacity C(W). If a channel W is split into two possibly correlated subchannels W1, W2, the capacity function always satisfies C(W1) + C(W2) ≤ C(W), while there are examples for which R0(W1) + R0(W2) > R0(W). The fact that cutoff rate can be "created" by channel splitting was noticed by Massey in his study of an optical modulation system. This paper gives a general framework for achieving similar gains in the cutoff rate of arbitrary DMCs by methods of channel combining and splitting. The emphasis is on simple schemes that can be implemented in practice. We give several examples that achieve significant gains in cutoff rate at little extra system complexity. Theoretically, as the complexity grows without bound, the proposed framework is capable of boosting the cutoff rate of a channel to arbitrarily close to its capacity in a sense made precise in the paper. Apart from Massey's work, the methods studied here have elements in common with Forney's concatenated coding idea, a method by Pinsker for cutoff rate improvement, and certain coded-modulation techniques, namely, Ungerboeck's set-partitioning idea and Imai-Hirakawa multilevel coding; these connections are discussed in the paper.
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    Cutoff rate for fixed-composition on-off keying over direct detection photon channels
    (1990) Toygar, M. Şenol.
    In this thesis, we consider direct detection photon channel with peak and average power constraints. This channel is modelled as a binary input discrete memoryless channel. We study the cutoff rate for different modulation formats on this channel since it is a measure of decoding complexity when sequential decoding is used and also, it gives an upper bound for the probability of error which decreases exponentially with the constraint length of convolutional code. Cutoff rates for the ensembles of fixed-composition and independent-letters codes along with ON-OFF keying are computed numerically and also some bounds are given. Cutoff rates versus signal-to-noise ratio or peak power are plotted for blocklengths of N=40,100 and for both ensembles. Comparison of cutoff rates for these two ensembles shows that for the direct detection photon channel the cutoff rate of fixed-composition ensemble is significantly greater than that of independent-letters ensemble for small values of signal-to-noise ratio and when the average power is a small fraction of peak power, say, 5-30%. In an uncoded system, for achieving a probability of error P(E)=(10 to the power -9), we should send 10 photons/slot with rate R=1 bit/slot, resulting in an efficiency of 0.1 bits/photon.However, using coding we can make probability of error arbitrarily small achieving an efficiency of 1 bit/photon. Also, some remarks on the implementation of fixed-composition trellis codes and on multi-level signalling instead of ON-OFF keying are given in conclusions.
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    On the reliability exponent of the exponential timing channel
    (IEEE, 2002) Arikan, E.
    We determine the reliability exponent E(R) of the Anantharam-Verdú exponential server timing channel with service rate μ for all rates R between a critical rate R c = (μ/4) log 2 and the channel capacity C = e -1μ. For rates between 0 and R c, we provide a random-coding lower bound E r(R) and a sphere-packing upper bound E sp(R) on E(R). We also determine that the cutoff rate R o for this channel equals μ/4, thus answering a question posed by Sundaresan and Verdú. An interesting aspect of our results is that the lower bound E r (R) for the reliability exponent of the timing channel coincides with Wyner's reliability exponent for the photon-counting channel with no dark current and with peak power constraint μ. Whether the reliability exponents of the two channels are actually equal everywhere remains open. This shows that the exponential server timing channel is at least as reliable as this type of a photon-counting channel for all rates.
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    Sequential decoding on intersymbol interference channels with application to magnetic recording
    (1990) Alanyalı, Murat
    In this work we treat sequential decoding in the problem of sequence estimation on intersymbol interference ( ISI ) channels. We consider the magnetic recording channel as the particular ISI channel and investigate the coding gains that can be achieved with sequential decoding for different information densities. Since the cutoff rate determines this quantity , we find lower bounds to the cutoff rate. The symmetric cutoff rate is computed as a theoretical lower bound and practical lower bounds are found through simulations. Since the optimum decoding metric is impractical, a sub-optimum metric has been used in the simulations. The results show that this metric can not achieve the cutoff rate in general, but still its performance is not far from that of the optimum metric. We compare the results to those of Immink[9] and see that one can achieve positive coding gains at information densities of practical interest where other practical codes used in magnetic recording show coding loss.