142 research outputs found
Feedback Communication Systems with Limitations on Incremental Redundancy
This paper explores feedback systems using incremental redundancy (IR) with
noiseless transmitter confirmation (NTC). For IR-NTC systems based on {\em
finite-length} codes (with blocklength ) and decoding attempts only at {\em
certain specified decoding times}, this paper presents the asymptotic expansion
achieved by random coding, provides rate-compatible sphere-packing (RCSP)
performance approximations, and presents simulation results of tail-biting
convolutional codes.
The information-theoretic analysis shows that values of relatively close
to the expected latency yield the same random-coding achievability expansion as
with . However, the penalty introduced in the expansion by limiting
decoding times is linear in the interval between decoding times. For binary
symmetric channels, the RCSP approximation provides an efficiently-computed
approximation of performance that shows excellent agreement with a family of
rate-compatible, tail-biting convolutional codes in the short-latency regime.
For the additive white Gaussian noise channel, bounded-distance decoding
simplifies the computation of the marginal RCSP approximation and produces
similar results as analysis based on maximum-likelihood decoding for latencies
greater than 200. The efficiency of the marginal RCSP approximation facilitates
optimization of the lengths of incremental transmissions when the number of
incremental transmissions is constrained to be small or the length of the
incremental transmissions is constrained to be uniform after the first
transmission. Finally, an RCSP-based decoding error trajectory is introduced
that provides target error rates for the design of rate-compatible code
families for use in feedback communication systems.Comment: 23 pages, 15 figure
Composite CDMA - A statistical mechanics analysis
Code Division Multiple Access (CDMA) in which the spreading code assignment
to users contains a random element has recently become a cornerstone of CDMA
research. The random element in the construction is particular attractive as it
provides robustness and flexibility in utilising multi-access channels, whilst
not making significant sacrifices in terms of transmission power. Random codes
are generated from some ensemble, here we consider the possibility of combining
two standard paradigms, sparsely and densely spread codes, in a single
composite code ensemble. The composite code analysis includes a replica
symmetric calculation of performance in the large system limit, and
investigation of finite systems through a composite belief propagation
algorithm. A variety of codes are examined with a focus on the high
multi-access interference regime. In both the large size limit and finite
systems we demonstrate scenarios in which the composite code has typical
performance exceeding sparse and dense codes at equivalent signal to noise
ratio.Comment: 23 pages, 11 figures, Sigma Phi 2008 conference submission -
submitted to J.Stat.Mec
Asymmetric Error Correction and Flash-Memory Rewriting using Polar Codes
We propose efficient coding schemes for two communication settings: 1.
asymmetric channels, and 2. channels with an informed encoder. These settings
are important in non-volatile memories, as well as optical and broadcast
communication. The schemes are based on non-linear polar codes, and they build
on and improve recent work on these settings. In asymmetric channels, we tackle
the exponential storage requirement of previously known schemes, that resulted
from the use of large Boolean functions. We propose an improved scheme, that
achieves the capacity of asymmetric channels with polynomial computational
complexity and storage requirement.
The proposed non-linear scheme is then generalized to the setting of channel
coding with an informed encoder, using a multicoding technique. We consider
specific instances of the scheme for flash memories, that incorporate
error-correction capabilities together with rewriting. Since the considered
codes are non-linear, they eliminate the requirement of previously known
schemes (called polar write-once-memory codes) for shared randomness between
the encoder and the decoder. Finally, we mention that the multicoding scheme is
also useful for broadcast communication in Marton's region, improving upon
previous schemes for this setting.Comment: Submitted to IEEE Transactions on Information Theory. Partially
presented at ISIT 201
Lossy source coding using belief propagation and soft-decimation over LDGM codes
This paper focus on the lossy compression of a binary symmetric source. We propose a new algorithm for binary quantization over low density generator matrix (LDGM) codes. The proposed algorithm is a modified version of the belief propagation (BP) algorithm used in the channel coding framework and has linear complexity in the code block length. We also provide a common framework under which the proposed algorithm and some previously proposed algorithms fit. Simulation results show that our scheme achieves close to state-of-the-art performance with reduced complexity
Performance Analysis of Quantum Error-Correcting Codes via MacWilliams Identities
One of the main challenges for an efficient implementation of quantum
information technologies is how to counteract quantum noise. Quantum error
correcting codes are therefore of primary interest for the evolution towards
quantum computing and quantum Internet. We analyze the performance of
stabilizer codes, one of the most important classes for practical
implementations, on both symmetric and asymmetric quantum channels. To this
aim, we first derive the weight enumerator (WE) for the undetectable errors of
stabilizer codes based on the quantum MacWilliams identities. The WE is then
used to evaluate the error rate of quantum codes under maximum likelihood
decoding or, in the case of surface codes, under minimum weight perfect
matching (MWPM) decoding. Our findings lead to analytical formulas for the
performance of generic stabilizer codes, including the Shor code, the Steane
code, as well as surface codes. For example, on a depolarizing channel with
physical error rate it is found that the logical error rate
is asymptotically for the
Shor code, for the
Steane code, for the surface
code, and for the surface
code.Comment: 25 pages, 5 figures, submitted to an IEEE journal. arXiv admin note:
substantial text overlap with arXiv:2302.1301
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