24,963 research outputs found
Unordered Error-Correcting Codes and their Applications
We give efficient constructions for error correcting
unordered {ECU) codes, i.e., codes such that any
pair of codewords are at a certain minimal distance
apart and at the same time they are unordered. These
codes are used for detecting a predetermined number
of (symmetric) errors and for detecting all unidirectional
errors. We also give an application in parallel
asynchronous communications
Exact and Approximate Expressions for the Probability of Undetected Error of Varshamov-Tenengol'ts Codes
Computation of the undetected error probability for error correcting codes
over the Z-channel is an important issue, explored only in part in previous
literature. In this paper we consider the case of Varshamov-Tenengol'ts codes,
by presenting some analytical, numerical, and heuristic methods for unveiling
this additional feature. Possible comparisons with Hamming codes are also shown
and discussed.Comment: 33 pages, 9 figures, 1 table. Submitted to the IEEE Transactions on
Information Theor
Density Evolution for Asymmetric Memoryless Channels
Density evolution is one of the most powerful analytical tools for
low-density parity-check (LDPC) codes and graph codes with message passing
decoding algorithms. With channel symmetry as one of its fundamental
assumptions, density evolution (DE) has been widely and successfully applied to
different channels, including binary erasure channels, binary symmetric
channels, binary additive white Gaussian noise channels, etc. This paper
generalizes density evolution for non-symmetric memoryless channels, which in
turn broadens the applications to general memoryless channels, e.g. z-channels,
composite white Gaussian noise channels, etc. The central theorem underpinning
this generalization is the convergence to perfect projection for any fixed size
supporting tree. A new iterative formula of the same complexity is then
presented and the necessary theorems for the performance concentration theorems
are developed. Several properties of the new density evolution method are
explored, including stability results for general asymmetric memoryless
channels. Simulations, code optimizations, and possible new applications
suggested by this new density evolution method are also provided. This result
is also used to prove the typicality of linear LDPC codes among the coset code
ensemble when the minimum check node degree is sufficiently large. It is shown
that the convergence to perfect projection is essential to the belief
propagation algorithm even when only symmetric channels are considered. Hence
the proof of the convergence to perfect projection serves also as a completion
of the theory of classical density evolution for symmetric memoryless channels.Comment: To appear in the IEEE Transactions on Information Theor
Variable-to-Fixed Length Homophonic Coding Suitable for Asymmetric Channel Coding
In communication through asymmetric channels the capacity-achieving input
distribution is not uniform in general. Homophonic coding is a framework to
invertibly convert a (usually uniform) message into a sequence with some target
distribution, and is a promising candidate to generate codewords with the
nonuniform target distribution for asymmetric channels. In particular, a
Variable-to-Fixed length (VF) homophonic code can be used as a suitable
component for channel codes to avoid decoding error propagation. However, the
existing VF homophonic code requires the knowledge of the maximum relative gap
of probabilities between two adjacent sequences beforehand, which is an
unrealistic assumption for long block codes. In this paper we propose a new VF
homophonic code without such a requirement by allowing one-symbol decoding
delay. We evaluate this code theoretically and experimentally to verify its
asymptotic optimality.Comment: Full version of the paper to appear in 2017 IEEE International
Symposium on Information Theory (ISIT2017
Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories
Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by â. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation
Efficient LLR Calculation for Non-Binary Modulations over Fading Channels
Log-likelihood ratio (LLR) computation for non-binary modulations over fading
channels is complicated. A measure of LLR accuracy on asymmetric binary
channels is introduced to facilitate good LLR approximations for non-binary
modulations. Considering piecewise linear LLR approximations, we prove
convexity of optimizing the coefficients according to this measure. For the
optimized approximate LLRs, we report negligible performance losses compared to
true LLRs.Comment: Submitted to IEEE Transactions on Communication
TTCM-aided rate-adaptive distributed source coding for Rayleigh fading channels
Adaptive turbo-trellis-coded modulation (TTCM)-aided asymmetric distributed source coding (DSC) is proposed, where two correlated sources are transmitted to a destination node. The first source sequence is TTCM encoded and is further compressed before it is transmitted through a Rayleigh fading channel, whereas the second source signal is assumed to be perfectly decoded and, hence, to be flawlessly shown at the destination for exploitation as side information for improving the decoding performance of the first source. The proposed scheme is capable of reliable communications within 0.80 dB of the Slepian-Wolf/Shannon (SW/S) theoretical limit at a bit error rate (BER) of 10-5. Furthermore, its encoder is capable of accommodating time-variant short-term correlation between the two sources
- âŚ