Variable-length channel codes with probabilistic delay guarantees

Abstract

Variable-length channel codes over discrete memoryless channels subject to probabilistic delay guarantees are examined in the non-vanishing error probability regime. Fundamental limits of these codes in several different settings, which depend on the availability of noiseless feedback and a termination option, are investigated. In stark contrast with average delay guarantees, the first-order terms of the fundamental limits turn out to be the same as those for fixed-length codes in all cases. Further, feedback is shown to improve the second-order term, even in the absence of a termination option.

On Error Exponents of Almost-Fixed-Length Channel Codes and Hypothesis Tests

“…Channel codes with probabilistic delay constraints were considered by Altug et al in [9], where they show that if the constraint on expected stopping time is replaced by a probabilistic one then the first order gain in rate ceases to exist. However, these works fail to notice the improvement in the error exponent achieved by codes under probabilistic delay constraints such as the class of almost-fixed-length codes over the class of fixed-length codes.…”

“…In other words, AFLF codes not only require the stopping time τ to be bounded in expectation but also require the probability that τ exceeds ℓ to be exponentially small. (iii) AFLF codes are a special case of VLF * codes considered by Altug et al in [9], where the condition on the stopping time…”

“…Polyanskiy et al in [18] show that for VLF channel codes feedback improves first and second-order terms of the logarithm of the maximum number of messages that can be transmitted with a non-vanishing error probability. Altug et al in [9] show that channel codes with more stringent constraints on stopping time, designed to reduce its variability, provide no such improvement even in the presence of feedback. Specifically, if the constraint on the expected value of the stopping time of VLF codes is replaced by a probabilistic one, given by equation ( 3), the first order gain in rate ceases to exist.…”

Variable-length Feedback Codes with Several Decoding Times for the Gaussian Channel

“…In [9], Kim et al consider VLSF codes where decoding must occur at a decoding time less than or equal to some constant and the decoding times satisfy n i = id for some d ∈ Z + . In [10], Altug et al modify the VLSF coding paradigm by replacing the average decoding time constraint with a constraint on the probability that the decoding time exceeds a target value; the benefit in the first-order term does not appear under this probabilistic delay constraint [10]. Truong and Tan [11], [12] extend the results in [6] to the Gaussian point-to-point and multiple access channels under an average power constraint.…”

Variable-Length Sparse Feedback Codes for Point-to-Point, Multiple Access, and Random Access Channels

“…In [9], Kim et al consider VLSF codes where decoding must occur at a decoding time less than or equal to some constant and the decoding times satisfy n i = id for some d ∈ Z + . In [10], Altug et al modify the VLSF coding paradigm by replacing the average decoding time constraint with a constraint on the probability that the decoding time exceeds a target value; the benefit in the first-order term does not appear under this probabilistic delay constraint [10]. Truong and Tan [11], [12] extend the results in [6] to the Gaussian point-to-point and multiple access channels under an average power constraint.…”