UCLA

This dissertation consists of three parts investigating the efficient reliable communication in the short blocklength regime for classical channels in three different settings: (i) no feedback, (ii) full, noiseless feedback, and (iii) finite, stop feedback.

The first part focuses on the non-feedback binary-input additive white Gaussian noise (AWGN) channel. A long-standing research problem is to design good linear block codes for this channel. As its primary contribution, we propose the cyclic-redundancy-check-aided (CRC-aided) convolutional code under serial list Viterbi decoding (SLVD). To design a good CRC-aided convolutional code, we propose the distance-spectrum optimal (DSO) CRC polynomial and provide an efficient search algorithm for a given convolutional code. We then analyze the performance and complexity of the SLVD for the CRC-aided convolutional code. For transmitting 64 information bits, simulation shows that some CRC-aided convolutional codes beat the random-coding union (RCU) bound at short blocklength.

The second part of the dissertation focuses on the binary asymmetric channel (BAC) with full, noiseless feedback, including the binary symmetric channel (BSC) as a special case. Building on the small-enough-difference (SED) coding scheme of Naghshvar et al. originally proposed for symmetric binary-input channels with feedback, we generalize the coding scheme to the class of BACs with feedback, and establish a non-asymptotic achievability bound for the deterministic variable-length feedback (VLF) code constructed from the generalized SED coding scheme. In the specific case of the BSC, we present a refined non-asymptotic VLF achievability bound. Despite the extreme use of feedback, Naghshvar et al.'s results on the BSC with full feedback appear to be inferior to Polyanskiy's bound for codes with a limited use of feedback, known as the variable-length stop-feedback (VLSF) codes. In contrast, numerical evaluations show that our VLF achievability bounds outperform Polyanskiy's VLSF achievability bound for both BAC and BSC cases.

The third part of the dissertation focuses on the performance of VLSF codes with finite optimal decoding times for the BI-AWGN channel. We first develop tight approximations on the tail probability of length-n cumulative information density which will play an important role in numerical evaluations. Building on a recent result of Yavas et al. on VLSF codes with finite decoding times, the problem reduces to an integer program of minimizing the upper bound of average blocklength subject to the average error probability, minimum gap, and integer constraints. By allowing real-valued decoding times and using a two-step minimization, we derive the gap-constrained sequential differential optimization procedure to numerically evaluate the achievability bound. Numerical evaluations show that Polyanskiy's bound for VLSF codes, which assumes infinite decoding times, can be closely approached with a finite (and relatively small) number of decoding times.