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LDPC Codes over the q-ary Multi-Bit Channel

Cohen, Rami and Raviv, Netanel and Cassuto, Yuval (2019) LDPC Codes over the q-ary Multi-Bit Channel. IEEE Transactions on Information Theory, 65 (7). pp. 4293-4306. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:20190228-152944857

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Abstract

In this paper, we introduce a new channel model termed as the q-ary multi-bit channel. This channel models a memory device, where q-ary symbols (q=2^s) are stored in the form of current/voltage levels. The symbols are read in a measurement process, which provides a symbol bit in each measurement step, starting from the most significant bit. An error event occurs when not all the symbol bits are known. To deal with such error events, we use GF(q) low-density parity-check (LDPC) codes and analyze their decoding performance. We start with iterative-decoding threshold analysis and derive optimal edge-label distributions for maximizing the decoding threshold. We later move to a finite-length iterative-decoding analysis and propose an edge-labeling algorithm for the improved decoding performance. We then provide a finite-length maximum-likelihood decoding analysis for both the standard non-binary random ensemble and LDPC ensembles. Finally, we demonstrate by simulations that the proposed edge-labeling algorithm improves the finite-length decoding performance by orders of magnitude.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/tit.2019.2900894DOIArticle
https://arxiv.org/abs/1706.09146arXivDiscussion Paper
ORCID:
AuthorORCID
Cohen, Rami0000-0002-9152-8446
Raviv, Netanel0000-0002-1686-1994
Cassuto, Yuval0000-0001-6369-6699
Additional Information:© 2018 IEEE. Manuscript received May 23, 2017; revised September 4, 2018; accepted February 4, 2019. Date of publication February 22, 2019; date of current version June 14, 2019. This work was supported in part by the Israel Science Foundation, in part by the U.S.–Israel Binational Science Foundation, and in part by the Henri Gutwirth Fund for Promotion of Research. This paper was presented in part at the 9th International Symposium on Turbo Codes and Iterative Information Processing and at the 2017 IEEE International Symposium on Information Theory.
Funders:
Funding AgencyGrant Number
Israel Science FoundationUNSPECIFIED
Binational Science Foundation (USA-Israel)UNSPECIFIED
Henri Gutwirth FundUNSPECIFIED
Subject Keywords:Low-density parity-check (LDPC) codes, q-ary codes, partial erasures, iterative decoding, decoding threshold, erasure channels, finite-length analysis
Record Number:CaltechAUTHORS:20190228-152944857
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190228-152944857
Official Citation:R. Cohen, N. Raviv and Y. Cassuto, "LDPC Codes Over the q-ary Multi-Bit Channel," in IEEE Transactions on Information Theory, vol. 65, no. 7, pp. 4293-4306, July 2019. doi: 10.1109/TIT.2019.2900894
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93365
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Feb 2019 23:38
Last Modified:18 Jun 2019 20:07

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