TY - GEN

T1 - MAC polar codes and matroids

AU - Abbe, Emmanuel

AU - Telatar, Emre

PY - 2010

Y1 - 2010

N2 - In this paper, a polar code for the m-user multiple access channel (MAC) with binary inputs is constructed. In particular, Arikan's polarization technique applied individually to each user polarizes any m-user binary input MAC into a finite collection of extremal MACs. The extremal MACs have a number of desirable properties: (i) the 'uniform sum rate'1 of the original channel is not lost, (ii) the extremal MACs have rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits; in this sense they are easy to communicate over. A polar code can then be constructed with an encoding and decoding complexity of O(n log n) (where n is the block length), a block error probability of o(exp(-n1/2-ε)), and capable of achieving the uniform sum rate of any binary input MAC with arbitrary many users. An application of this polar code construction to a coding scheme for the AWGN channel is also discussed.

AB - In this paper, a polar code for the m-user multiple access channel (MAC) with binary inputs is constructed. In particular, Arikan's polarization technique applied individually to each user polarizes any m-user binary input MAC into a finite collection of extremal MACs. The extremal MACs have a number of desirable properties: (i) the 'uniform sum rate'1 of the original channel is not lost, (ii) the extremal MACs have rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits; in this sense they are easy to communicate over. A polar code can then be constructed with an encoding and decoding complexity of O(n log n) (where n is the block length), a block error probability of o(exp(-n1/2-ε)), and capable of achieving the uniform sum rate of any binary input MAC with arbitrary many users. An application of this polar code construction to a coding scheme for the AWGN channel is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=77952689242&partnerID=8YFLogxK

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U2 - 10.1109/ITA.2010.5454148

DO - 10.1109/ITA.2010.5454148

M3 - Conference contribution

AN - SCOPUS:77952689242

SN - 9781424470143

T3 - 2010 Information Theory and Applications Workshop, ITA 2010 - Conference Proceedings

SP - 8

EP - 15

BT - 2010 Information Theory and Applications Workshop, ITA 2010 - Conference Proceedings

T2 - 2010 Information Theory and Applications Workshop, ITA 2010

Y2 - 31 January 2010 through 5 February 2010

ER -