BER estimation of a MLSE using the union bound

2005 ◽  
Author(s):  
C. Xie ◽  
P. Mai ◽  
F.N. Hauske ◽  
B. Lankl ◽  
E.-D. Schmidt
Keyword(s):  
Union Bound

Asymptotics of the Random Coding Union Bound

2018 ◽  
Author(s):  
Josep Font-Segura ◽  
Alfonso Martinez ◽  
Albert Guillen i Fabregas
Keyword(s):  
Random Coding ◽  
Union Bound

scholarly journals Sequential decoding of a general classical-quantum channel

2013 ◽  
Vol 469 (2157) ◽  
pp. 20130259 ◽  
Author(s):  
Mark M. Wilde
Keyword(s):  
Quantum Measurement ◽  
Failure Probability ◽  
High Probability ◽  
Polar Codes ◽  
Sequential Decoding ◽  
Single Instance ◽  
Small Failure Probability ◽  
Classical Quantum ◽  
Union Bound ◽  
Sequential Measurements

Because a quantum measurement generally disturbs the state of a quantum system, one might think that it should not be possible for a sender and receiver to communicate reliably when the receiver performs a large number of sequential measurements to determine the message of the sender. We show here that this intuition is not true, by demonstrating that a sequential decoding strategy works well even in the most general ‘one-shot’ regime, where we are given a single instance of a channel and wish to determine the maximal number of bits that can be communicated up to a small failure probability. This result follows by generalizing a non-commutative union bound to apply for a sequence of general measurements. We also demonstrate two ways in which a receiver can recover a state close to the original state after it has been decoded by a sequence of measurements that each succeed with high probability. The second of these methods will be useful in realizing an efficient decoder for fully quantum polar codes, should a method ever be found to realize an efficient decoder for classical-quantum polar codes.

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