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1. Achievable Rates for Low-Complexity Posterior Matching over the Binary Symmetric Channel

   https://doi.org/10.1109/TIT.2023.3322095  

   Antonini, Amaael; Gimelshein, Rita; Wesel, Richard (October 2023, IEEE Transactions on Information Theory)

   Horstein, Burnashev, Shayevitz and Feder, Naghshvar et al . and others have studied sequential transmission of a k-bit message over the binary symmetric channel (BSC) with full, noiseless feedback using posterior matching. Yang et al . provide an improved lower bound on the achievable rate using martingale analysis that relies on the small-enough difference (SED) partitioning introduced by Naghshvar et al . SED requires a relatively complex encoder and decoder. To reduce complexity, this paper replaces SED with relaxed constraints that admit the small enough absolute difference (SEAD) partitioning rule. The main analytical results show that achievable-rate bounds higher than those found by Yang et al . [2] are possible even under the new constraints, which are less restrictive than SED. The new analysis does not use martingale theory for the confirmation phase and applies a surrogate channel technique to tighten the results. An initial systematic transmission further increases the achievable rate bound. The simplified encoder associated with SEAD has a complexity below order O ( K 2 ) and allows simulations for message sizes of at least 1000 bits. For example, simulations achieve 99% of of the channel’s 0.50-bit capacity with an average block size of 200 bits for a target codeword error rate of 10 -3. 

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2. Low Complexity Algorithms for Transmission of Short Blocks over the BSC with Full Feedback

   https://doi.org/10.1109/ISIT44484.2020.9174232  

   Antonini, Amaael; Yang, Hengjie; Wesel, Richard D. (June 2020, 2020 IEEE International Symposium on Information Theory (ISIT))

   null (Ed.)

   Building on the work of Horstein, Shayevitz and Feder, and Naghshvar et al., this paper presents algorithms for low-complexity sequential transmission of a k-bit message over the binary symmetric channel (BSC) with full, noiseless feedback. To lower complexity, this paper shows that the initial k binary transmissions can be sent before any feedback is required and groups messages with equal posteriors to reduce the number of posterior updates from exponential in k to linear in k. Simulation results demonstrate that achievable rates for this full, noiseless feedback system approach capacity rapidly as a function of average blocklength, faster than known finite-blocklength lower bounds on achievable rate with noiseless active feedback and significantly faster than finite-blocklength lower bounds for a stop feedback system. 

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3. Variable-Length Stop-Feedback Codes With Finite Optimal Decoding Times for BI-AWGN Channels

   https://doi.org/10.1109/ISIT50566.2022.9834526  

   Yang, Hengjie; Yavas, Recep Can; Kostina, Victoria; Wesel, Richard D. (June 2022, 2022 IEEE International Symposium on Information Theory (ISIT))

   In this paper, we are interested in the performance of a variable-length stop-feedback (VLSF) code with m optimal decoding times for the binary-input additive white Gaussian noise channel. We first develop tight approximations to the tail probability of length-n cumulative information density. Building on the work of Yavas et al., for a given information density threshold, we formulate the integer program of minimizing the upper bound on average blocklength over all decoding times subject to the average error probability, minimum gap and integer constraints. Eventually, minimization of locally optimal upper bounds over all thresholds yields the globally minimum upper bound and the above method is called the two-step minimization. Relaxing to allow positive real-valued decoding times activates the gap constraint. We develop gap-constrained sequential differential optimization (SDO) procedure to find the optimal, gap-constrained, real-valued decoding times. In the error regime of practical interest, Polyanskiy's scheme of stopping at zero does not help. In this region, the achievability bounds estimated by the two-step minimization and gap-constrained SDO show that Polyanskiy’s achievability bound for VLSF codes can be approached with a small number of decoding times. 

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4. Rate of Prefix-free Codes in LQG Control Systems with Side Information

   Cuvelier, T.C. & (March 2021, Annual Conference on Information Sciences and Systems (CISS))

   In this work, we study an LQG control system where one of two feedback channels is discrete and incurs a communication cost. We assume that a decoder (co-located with the controller) can make noiseless measurements of a subset of the state vector (referred to as side information) meanwhile a remote encoder (co-located with a sensor) can make arbitrary measurements of the entire state vector, but must convey its measurements to the decoder over a noiseless binary channel. Use of the channel incurs a communication cost, quantified as the time-averaged expected length of prefix-free binary codeword. We study the tradeoff between the communication cost and control performance. The formulation motivates a constrained directed information minimization problem, which can be solved via convex optimization. Using the optimization, we propose a quantizer design and a subsequent achievability result. 

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5. Finite-Blocklength and Error-Exponent Analyses for LDPC Codes in Point-to-Point and Multiple Access Communication

   https://doi.org/10.1109/ISIT44484.2020.9173963  

   Liu, Yuxin; Effros, Michelle (June 2020, 2020 IEEE International Symposium on Information Theory (ISIT))

   null (Ed.)

   This paper applies error-exponent and dispersionstyle analyses to derive finite-blocklength achievability bounds for low-density parity-check (LDPC) codes over the point-to-point channel (PPC) and multiple access channel (MAC). The error-exponent analysis applies Gallager's error exponent to bound achievable symmetrical and asymmetrical rates in the MAC. The dispersion-style analysis begins with a generalization of the random coding union (RCU) bound from random code ensembles with i.i.d. codewords to random code ensembles in which codewords may be statistically dependent; this generalization is useful since the codewords of random linear codes such as LDPC codes are dependent. Application of the RCU bound yields finite-blocklength error bounds and asymptotic achievability results for both i.i.d. random codes and LDPC codes. For discrete, memoryless channels, these results show that LDPC codes achieve first- and second-order performance that is optimal for the PPC and identical to the best prior results for the MAC. 

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