Title :
Coding over an erasure channel with a large alphabet size
Author :
Fashandi, Shervan ; Gharan, Shahab Oveis ; Khandani, Amir K.
Author_Institution :
ECE Dept., Univ. of Waterloo, Waterloo, ON
Abstract :
An erasure channel with a fixed alphabet size q, where q Gt 1, is studied. It is proved that over any erasure channel (with or without memory), maximum distance separable (MDS) codes achieve the minimum probability of error (assuming maximum likelihood decoding). Assuming a memoryless erasure channel, the error exponent of MDS codes are compared with that of random codes. It is shown that the envelopes of these two exponents are identical for rates above the critical rate. Noting the optimality of MDS codes, it is concluded that random coding is exponentially optimal as long as the block size N satisfies N < q + 1.
Keywords :
block codes; error statistics; maximum likelihood decoding; random codes; MDS codes; block size; error exponent; large alphabet size; maximum distance separable codes; maximum likelihood decoding; memoryless erasure channel; minimum error probability; random coding; Block codes; Channel capacity; Councils; Discrete Fourier transforms; Error probability; Galois fields; Internet; Maximum likelihood decoding;
Conference_Titel :
Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Conference_Location :
Toronto, ON
Print_ISBN :
978-1-4244-2256-2
Electronic_ISBN :
978-1-4244-2257-9
DOI :
10.1109/ISIT.2008.4595148
