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

This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ L decoding times n ₁ , n ₂ ,…, n_L for the point-to-point and multiple access channels and KL + 1 decoding times for the random access channel with at most K active transmitters. In the point-to-point and multiple access channels, the decoder uses the observed channel outputs to decide whether to decode at each of the allowed decoding times n ₁ ,…, n_L , at each time telling the encoder whether or not to stop transmitting using a single bit of feedback. In the random access scenario, the decoder estimates the number of active transmitters at time n ₀ and then chooses among decoding times n _k,1 ,…, n _k,L if it believes that there are k active transmitters. In all cases, the choice of allowed decoding times is part of the code design; given fixed value L , allowed decoding times are chosen to minimize the expected decoding time for a given codebook size and target average error probability. The number L in each scenario is assumed to be constant even when the blocklength is allowed to grow; the resulting code therefore requires only sparse feedback. The central results are asymptotic approximations of achievable rates as a function of the error probability, the expected decoding time, and the number of decoding times. A converse for variable-length stop-feedback codes with uniformly-spaced decoding times is included for the point-to-point channel.