18 research outputs found
Write Channel Model for Bit-Patterned Media Recording
We propose a new write channel model for bit-patterned media recording that
reflects the data dependence of write synchronization errors. It is shown that
this model accommodates both substitution-like errors and insertion-deletion
errors whose statistics are determined by an underlying channel state process.
We study information theoretic properties of the write channel model, including
the capacity, symmetric information rate, Markov-1 rate and the zero-error
capacity.Comment: 11 pages, 12 figures, journa
Achievable Rates for Noisy Channels with Synchronization Errors
Cataloged from PDF version of article.We develop several lower bounds on the capacity of binary input symmetric output channels with synchronization errors, which also suffer from other types of impairments such as substitutions, erasures, additive white Gaussian noise (AWGN), etc. More precisely, we show that if a channel suffering from synchronization errors as well as other type of impairments can be decomposed into a cascade of two component channels where the first one is another channel with synchronization errors and the second one is a memoryless channel (with no synchronization errors), a lower bound on the capacity of the original channel in terms of the capacity of the component synchronization error channel can be derived. A primary application of our results is that we can employ any lower bound derived on the capacity of the component synchronization error channel to find lower bounds on the capacity of the (original) noisy channel with synchronization errors. We apply the general ideas to several specific classes of channels such as synchronization error channels with erasures and substitutions, with symmetric q-ary outputs and with AWGN explicitly, and obtain easy-to-compute bounds. We illustrate that, with our approach, it is possible to derive tighter capacity lower bounds compared to the currently available bounds in the literature for certain classes of channels, e.g., deletion/substitution channels and deletion/AWGN channels (for certain signal-to-noise ratio (SNR) ranges). © 2014 IEEE
Capacity Bounds and Concatenated Codes Over Segmented Deletion Channels
Cataloged from PDF version of article.We develop an information theoretic characterization
and a practical coding approach for segmented deletion
channels. Compared to channels with independent and identically
distributed (i.i.d.) deletions, where each bit is independently
deleted with an equal probability, the segmentation assumption
imposes certain constraints, i.e., in a block of bits of a certain
length, only a limited number of deletions are allowed to occur.
This channel model has recently been proposed and motivated
by the fact that for practical systems, when a deletion error
occurs, it is more likely that the next one will not appear
very soon. We first argue that such channels are information
stable, hence their channel capacity exists. Then, we introduce
several upper and lower bounds with two different methods in an
attempt to understand the channel capacity behavior. The first
scheme utilizes certain information provided to the transmitter
and/or receiver while the second one explores the asymptotic
behavior of the bounds when the average bit deletion rate is
small. In the second part of the paper, we consider a practical
channel coding approach over a segmented deletion channel.
Specifically, we utilize outer LDPC codes concatenated with inner
marker codes, and develop suitable channel detection algorithms
for this scenario. Different maximum-a-posteriori (MAP) based
channel synchronization algorithms operating at the bit and
symbol levels are introduced, and specific LDPC code designs are
explored. Simulation results clearly indicate the advantages of the
proposed approach. In particular, for the entire range of deletion
probabilities less than unity, our scheme offers a significantly
larger transmission rate compared to the other existing solutions
in the literature
A Lower Bound on the List-Decodability of Insdel Codes
For codes equipped with metrics such as Hamming metric, symbol pair metric or
cover metric, the Johnson bound guarantees list-decodability of such codes.
That is, the Johnson bound provides a lower bound on the list-decoding radius
of a code in terms of its relative minimum distance , list size and
the alphabet size For study of list-decodability of codes with insertion
and deletion errors (we call such codes insdel codes), it is natural to ask the
open problem whether there is also a Johnson-type bound. The problem was first
investigated by Wachter-Zeh and the result was amended by Hayashi and Yasunaga
where a lower bound on the list-decodability for insdel codes was derived.
The main purpose of this paper is to move a step further towards solving the
above open problem. In this work, we provide a new lower bound for the
list-decodability of an insdel code. As a consequence, we show that unlike the
Johnson bound for codes under other metrics that is tight, the bound on
list-decodability of insdel codes given by Hayashi and Yasunaga is not tight.
Our main idea is to show that if an insdel code with a given Levenshtein
distance is not list-decodable with list size , then the list decoding
radius is lower bounded by a bound involving and . In other words, if
the list decoding radius is less than this lower bound, the code must be
list-decodable with list size . At the end of the paper we use such bound to
provide an insdel-list-decodability bound for various well-known codes, which
has not been extensively studied before