29,777 research outputs found
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
Rewriting Flash Memories by Message Passing
This paper constructs WOM codes that combine rewriting and error correction
for mitigating the reliability and the endurance problems in flash memory. We
consider a rewriting model that is of practical interest to flash applications
where only the second write uses WOM codes. Our WOM code construction is based
on binary erasure quantization with LDGM codes, where the rewriting uses
message passing and has potential to share the efficient hardware
implementations with LDPC codes in practice. We show that the coding scheme
achieves the capacity of the rewriting model. Extensive simulations show that
the rewriting performance of our scheme compares favorably with that of polar
WOM code in the rate region where high rewriting success probability is
desired. We further augment our coding schemes with error correction
capability. By drawing a connection to the conjugate code pairs studied in the
context of quantum error correction, we develop a general framework for
constructing error-correction WOM codes. Under this framework, we give an
explicit construction of WOM codes whose codewords are contained in BCH codes.Comment: Submitted to ISIT 201
When Do WOM Codes Improve the Erasure Factor in Flash Memories?
Flash memory is a write-once medium in which reprogramming cells requires
first erasing the block that contains them. The lifetime of the flash is a
function of the number of block erasures and can be as small as several
thousands. To reduce the number of block erasures, pages, which are the
smallest write unit, are rewritten out-of-place in the memory. A Write-once
memory (WOM) code is a coding scheme which enables to write multiple times to
the block before an erasure. However, these codes come with significant rate
loss. For example, the rate for writing twice (with the same rate) is at most
0.77.
In this paper, we study WOM codes and their tradeoff between rate loss and
reduction in the number of block erasures, when pages are written uniformly at
random. First, we introduce a new measure, called erasure factor, that reflects
both the number of block erasures and the amount of data that can be written on
each block. A key point in our analysis is that this tradeoff depends upon the
specific implementation of WOM codes in the memory. We consider two systems
that use WOM codes; a conventional scheme that was commonly used, and a new
recent design that preserves the overall storage capacity. While the first
system can improve the erasure factor only when the storage rate is at most
0.6442, we show that the second scheme always improves this figure of merit.Comment: to be presented at ISIT 201
Write-Once-Memory Codes by Source Polarization
We propose a new Write-Once-Memory (WOM) coding scheme based on source
polarization. By applying a source polarization transformation on the
to-be-determined codeword, the proposed WOM coding scheme encodes information
into the bits in the high-entropy set. We prove in this paper that the proposed
WOM codes are capacity-achieving. WOM codes have found many applications in
modern data storage systems, such as flash memories.Comment: 5 pages, Proceedings of the International Conference on Computing,
Networking and Communications (ICNC 2015), Anaheim, California, USA, February
16-19, 201
Scalable Successive-Cancellation Hardware Decoder for Polar Codes
Polar codes, discovered by Ar{\i}kan, are the first error-correcting codes
with an explicit construction to provably achieve channel capacity,
asymptotically. However, their error-correction performance at finite lengths
tends to be lower than existing capacity-approaching schemes. Using the
successive-cancellation algorithm, polar decoders can be designed for very long
codes, with low hardware complexity, leveraging the regular structure of such
codes. We present an architecture and an implementation of a scalable hardware
decoder based on this algorithm. This design is shown to scale to code lengths
of up to N = 2^20 on an Altera Stratix IV FPGA, limited almost exclusively by
the amount of available SRAM
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