A note on the decoding complexity of error-correcting codes
Information Processing Letters
Discrete Applied Mathematics
Synchronization of passifiable Lurie systems via limited-capacity communication channel
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Capacity-achieving codes with bounded graphical complexity and maximum likelihood decoding
IEEE Transactions on Information Theory
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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A bound on the minimum distance of a binary error-correcting code is established given constraints on the computational time-space complexity of its encoder where the encoder is modeled as a branching program. The bound obtained asserts that if the encoder uses linear time and sublinear memory in the most general sense, then the minimum distance of the code cannot grow linearly with the block length when the rate is nonvanishing, that is, the minimum relative distance of the code tends to zero in such a setting. The setting is general enough to include nonserially concatenated turbo-like codes and various generalizations. Our argument is based on branching program techniques introduced by Ajtai. The case of constant-depth AND-OR circuit encoders with unbounded fanins are also considered.