Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider rate R = k over n causal linear codes that map a sequence of k-dimensional binary vectors {b t } t  ∞ =0 to a sequence of n-dimensional binary vectors {c t } t  ∞ =0, such that each c t  is a function of {b τ } τ  t =0. Such a code is called anytime reliable, for a particular binary-input memoryless channel, if at each time instant t, and for all delays d ≥ d o , the probability of error equation decays exponentially in d, i.e., equation, for some β > 0. Anytime reliable codes are useful in interactive communication problems and, in particular, can be used to stabilize unstable plants across noisy channels. Schulman proved the existence of such codes which, due to their structure, he called tree codes in [1]; hover, to date, no explicit constructions and tractable decoding algorithms have been devised. ,  show the existence of anytime reliable “linear” codes with “high probability”, i.e., suitably chosen random linear causal codes are anytime reliable with high probability. The key is to consider time-invariant codes (i.e., ones with Toeplitz generator and parity check matrices) which obviates the need to union bound over all times. For the binary erasure channel  give a simple ML decoding algorithm whose average complexity is constant per time instant and for which the probability that complexity at a given time t exceeds KC 3  decays exponentially in C.  show the efficacy of the method by simulating the stabilization of an unstable plant across a BEC, and remark on the tradeoffs beten the utilization of the communication resources and the control performance.
['Ravi Teja Sukhavasi', 'Babak Hassibi']
I am writing a research paper on a idea Linear error correcting codes with anytime reliability
[{"from": "human", "value": "I am writing a research paper on a idea Linear error correcting codes with anytime reliability"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider rate R = k over n causal linear codes that map a sequence of k-dimensional binary vectors {b t } t  \u221e =0 to a sequence of n-dimensional binary vectors {c t } t  \u221e =0, such that each c t  is a function of {b \u03c4 } \u03c4  t =0. Such a code is called anytime reliable, for a particular binary-input memoryless channel, if at each time instant t, and for all delays d \u2265 d o , the probability of error equation decays exponentially in d, i.e., equation, for some \u03b2 > 0. Anytime reliable codes are useful in interactive communication problems and, in particular, can be used to stabilize unstable plants across noisy channels. Schulman proved the existence of such codes which, due to their structure, he called tree codes in [1]; hover, to date, no explicit constructions and tractable decoding algorithms have been devised. ,  show the existence of anytime reliable \u201clinear\u201d codes with \u201chigh probability\u201d, i.e., suitably chosen random linear causal codes are anytime reliable with high probability. The key is to consider time-invariant codes (i.e., ones with Toeplitz generator and parity check matrices) which obviates the need to union bound over all times. For the binary erasure channel  give a simple ML decoding algorithm whose average complexity is constant per time instant and for which the probability that complexity at a given time t exceeds KC 3  decays exponentially in C.  show the efficacy of the method by simulating the stabilization of an unstable plant across a BEC, and remark on the tradeoffs beten the utilization of the communication resources and the control performance."}]