TY - JOUR

T1 - Improved Constructions of Coding Schemes for the Binary Deletion Channel and the Poisson Repeat Channel

AU - Con, Roni

AU - Shpilka, Amir

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2022/5/1

Y1 - 2022/5/1

N2 - This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter p (BDC p) every bit is deleted independently with probability p. A lower bound of (1-p)/9 is known on the capacity of the BDC p , yet no explicit construction is known to achieve this rate. We give an explicit family of codes of rate (1-p)/16 , for every p. This improves upon the work of Guruswami and Li (2018) that gave a construction of rate (1-p)/120. The codes in our family have polynomial time encoding and decoding algorithms. Another channel considered in this work is the Poisson repeat channel with parameter λ (PRC λ) in which every bit is replaced with a discrete Poisson number of copies of that bit, where the number of copies has mean λ . We show that our construction works for this channel as well. As far as we know, this is the first explicit construction of an error correcting code for PRC λ.

AB - This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter p (BDC p) every bit is deleted independently with probability p. A lower bound of (1-p)/9 is known on the capacity of the BDC p , yet no explicit construction is known to achieve this rate. We give an explicit family of codes of rate (1-p)/16 , for every p. This improves upon the work of Guruswami and Li (2018) that gave a construction of rate (1-p)/120. The codes in our family have polynomial time encoding and decoding algorithms. Another channel considered in this work is the Poisson repeat channel with parameter λ (PRC λ) in which every bit is replaced with a discrete Poisson number of copies of that bit, where the number of copies has mean λ . We show that our construction works for this channel as well. As far as we know, this is the first explicit construction of an error correcting code for PRC λ.

KW - Binary deletion channel

KW - Channel capacity

KW - Error correcting codes

UR - http://www.scopus.com/inward/record.url?scp=85124191750&partnerID=8YFLogxK

U2 - 10.1109/TIT.2022.3148190

DO - 10.1109/TIT.2022.3148190

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AN - SCOPUS:85124191750

SN - 0018-9448

VL - 68

SP - 2920

EP - 2940

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -