TY - GEN

T1 - Deterministic rateless codes for BSC [extended abstract]

AU - Applebaum, Benny

AU - David, Liron

AU - Even, Guy

PY - 2015/1/11

Y1 - 2015/1/11

N2 - A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for every channel in the family, reliable communication is obtained by a prefix of the code whose rate is arbitrarily close to the channel's capacity. As a result, a universal encoder can communicate over all channels in the family while simultaneously achieving optimal communication overhead. In this paper, we construct the first deterministic rateless code for the binary symmetric channel. Our code can be encoded and decoded in O(β) time per bit and in almost logarithmic parallel time of O(β log n), where β is any (arbitrarily slow) super-constant function. Furthermore, the error probability of our code is almost exponentially small exp(-Ω(n/β)). Previous rateless codes are probabilistic (i.e., based on code ensembles), require polynomial time per bit for decoding, and have inferior asymptotic error probabilities. Our main technical contribution is a constructive proof for the existence of an infinite generating matrix that each of its prefixes induce a weight distribution that approximates the expected weight distribution of a random linear code.

AB - A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for every channel in the family, reliable communication is obtained by a prefix of the code whose rate is arbitrarily close to the channel's capacity. As a result, a universal encoder can communicate over all channels in the family while simultaneously achieving optimal communication overhead. In this paper, we construct the first deterministic rateless code for the binary symmetric channel. Our code can be encoded and decoded in O(β) time per bit and in almost logarithmic parallel time of O(β log n), where β is any (arbitrarily slow) super-constant function. Furthermore, the error probability of our code is almost exponentially small exp(-Ω(n/β)). Previous rateless codes are probabilistic (i.e., based on code ensembles), require polynomial time per bit for decoding, and have inferior asymptotic error probabilities. Our main technical contribution is a constructive proof for the existence of an infinite generating matrix that each of its prefixes induce a weight distribution that approximates the expected weight distribution of a random linear code.

KW - Binary symmetric channel

KW - Capacity achieving error correcting code

KW - Rateless codes

UR - http://www.scopus.com/inward/record.url?scp=84922203180&partnerID=8YFLogxK

U2 - 10.1145/2688073.2688117

DO - 10.1145/2688073.2688117

M3 - פרסום בספר כנס

AN - SCOPUS:84922203180

T3 - ITCS 2015 - Proceedings of the 6th Innovations in Theoretical Computer Science

SP - 31

EP - 40

BT - ITCS 2015 - Proceedings of the 6th Innovations in Theoretical Computer Science

PB - Association for Computing Machinery, Inc

Y2 - 11 January 2015 through 13 January 2015

ER -