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Semantic SCL Decoding for Polar Codes

Andy Huang, Chentao Yue, Branka Vucetic, Yonghui Li

arXiv:2610.34729v1cs.ITmath.IT

TL;DR

Conventional channel decoding treats information bits as uniform and independent, despite residual structure in transmitted text. This paper incorporates byte-level language-model priors into polar-code SCL path metrics and reports lower BLER than CA-SCL. Selective guidance can reduce decoding time while trading off error-rate performance.

  • Problem

    Conventional channel decoding treats information bits as uniform and independent, although transmitted source data often retains redundancy that could be exploited.

    Source: §I · p. 1

  • Method

    A fine-tuned byte-level language model supplies next-byte priors that become conditional bit costs added to SCL path metrics before pruning, with optional guidance limited to unreliable bytes.

    Source: §I · p. 1, D. Threshold-Based LM Guidance · p. 3

  • Results

    At R = 0.75 and L = 16, BLER decreases from 6.31 × 10−1 to 3.68 × 10−3 at Eb/N0 = 1.5 dB, while selective guidance reduces decoding time by about two thirds at a loss of about 0.2 dB.

    Source: B. BLER Analysis · p. 5, §V · p. 6

  • Takeaways & Limitations

    With L = 8, Semantic SCL outperforms CA-SCL with L = 256 while requiring about one quarter of its decoding time in the evaluated software implementation.

    Source: C. Latency · p. 5, §V · p. 6

    Reported latency comparisons are specific to the software implementation and need not reflect the relative cost of dedicated hardware decoders.

    Source: C. Latency · p. 5

Abstract

from arXiv · show

Semantic error control coding (SECC) has emerged as a promising paradigm for improving communication reliability by exploiting the inherent structure and semantic dependencies of transmitted information. This paper proposes a semantic successive cancellation list (SCL) decoder for polar codes carrying natural-language text. A fine-tuned byte-level language model provides next-byte priors, which are converted into conditional bit costs and incorporated directly into the SCL path metric before each pruning step. This allows the decoder to jointly exploit channel reliability and source structure while retaining the conventional polar coding framework. The language model can also be invoked only for bytes whose channel decisions are unreliable, trading decoding performance for latency. Simulations for length-512 polar codes show substantial block error rate (BLER) improvements over conventional CRC-aided SCL (CA-SCL) decoding. At rate R=0.75 and list size L=16, the proposed decoder achieves more than 1 dB of gain in BLER compared to CA-SCL with the same L. Moreover, with L=8, it outperforms conventional CA-SCL with L=256 in terms of BLER, while requiring about one quarter of the decoding time of the latter in the evaluated software implementation.

I. INTRODUCTION

Conventional channel decoding treats information bits as uniform and independent, although transmitted text retains exploitable structure. The paper introduces language-model-aided SCL decoding for polar-coded text and evaluates it in a length-512 AWGN setting.

I. INTRODUCTION

  • Unlike end-to-end JSCC, SECC retains the existing channel-coding scheme while optimizing decoding to exploit learned source information [7].Prior LM-aided decoders had not targeted polar codes, while a dictionary prior for polar-coded text ignores context beyond the current word and is confined to its stored vocabulary [8], [9],,.Source: §I · p. 1
  • A fine-tuned ByT5 model supplies next-byte probabilities, converted into conditional bit costs and added to path metrics before each pruning step.Guidance can be restricted to bytes whose channel LLR magnitudes fall below threshold T.Source: §I · p. 1
  • At R = 0.75 and L = 16, BLER falls from 6.31×10−1 to 3.68×10−3 at Eb/N0 = 1.5 dB; selective guidance cuts decoding time by about two thirds at a loss of about 0.2 dB.The decoder is evaluated with length-512 polar codes and a 16-bit CRC.Source: §I · pp. 1–2

A. System Model

  • The system transmits text payload bytes with an appended 16-bit CRC through a polar code, BPSK modulation, and an AWGN channel.The evaluated setup uses ASCII bytes and the receiver estimates the text from the noisy signal.Source: A. System Model · p. 2

B. Polar Encoding

Polar encoding places information and CRC bits in selected reliable bit-channels and maps the resulting vector to a codeword. CA-SCL maintains candidate paths during sequential decoding and uses the CRC to select among survivors.

B. Polar Encoding

  • The polar code selects K reliable bit-channels from N = 2^m positions for information, while the remaining positions are frozen to known values.The K information bits, comprising payload and CRC, are placed in increasing index order.Source: B. Polar Encoding · p. 2
  • The generator matrix is G_N = B_NF^⊗m, and the codeword is c = uG_N with operations over GF(2).The input vector contains information or CRC bits at selected positions and frozen bits elsewhere.Source: B. Polar Encoding · p. 2

C. CRC-Aided Successive Cancellation List Decoding

  • SCL branches each path at information positions, ranks candidates by cumulative channel path metric, and retains the L smallest-metric paths when the list grows too large.SC makes sequential decisions from the received vector and preceding decisions; an early error may propagate to later bits.Source: C. CRC-Aided Successive Cancellation… · p. 2
  • CA-SCL checks surviving paths against the appended CRC, selecting the lowest-metric CRC-valid path or the lowest-metric path if none passes..Source: C. CRC-Aided Successive Cancellation… · p. 2

D. ByT5 Language-Model Priors

The decoder uses ByT5 as a byte-level language model to estimate linguistic plausibility from preceding bytes. Its next-byte probabilities supply a prior for decoding candidate text sequences.

D. ByT5 Language-Model Priors

  • ByT5 operates directly on UTF-8 bytes rather than word- or subword-level tokens.The paper uses the decoder of ByT5-small for causal byte-level modeling, with the encoder input fixed to a padding token.Source: D. ByT5 Language-Model Priors · p. 2
  • Given preceding bytes t<j, the model outputs a probability distribution over the next byte tj.The model’s logits are normalized over the 256 byte values, excluding special tokens.Source: D. ByT5 Language-Model Priors · p. 2
  • The conditional probabilities quantify candidate sequences’ linguistic plausibility and serve as a language-model prior during decoding.The probability of a byte prefix follows from the chain rule.Source: D. ByT5 Language-Model Priors · p. 3

III. PROPOSED SEMANTIC SCL DECODER

Semantic SCL modifies CA-SCL path ranking by combining channel evidence with a language-model prior. The language-model contribution is weighted and accumulated alongside the channel metric.

A. LM-Aided Path Metric

  • Candidate paths are ranked using both channel evidence and a language-model prior rather than the CA-SCL procedure’s channel evidence alone.The decoder retains the L candidates with the smallest combined metrics whenever the list exceeds L.Source: A. LM-Aided Path Metric · p. 3
  • The combined metric adds the language-model cost to the channel metric with weight α, which controls their relative contribution.The LM does not directly observe the received signal y.Source: A. LM-Aided Path Metric · p. 3
  • When α = 0, the decoder bypasses language-model inference and uses conventional CA-SCL decoding..Source: A. LM-Aided Path Metric · p. 3

B. Byte Priors and Bit Costs

The decoder obtains a next-byte distribution for each surviving path and converts it into bitwise language costs before pruning. These costs accumulate to the byte’s negative log-prior and combine with the channel metric.

B. Byte Priors and Bit Costs

  • Each surviving path’s preceding-byte prefix is supplied to ByT5 for a next-byte distribution, reused across that byte’s eight payload-bit decisions.The paths are evaluated together in a batch.Source: B. Byte Priors and Bit Costs · p. 3
  • At each bit, the language cost reflects the probability of that bit conditioned on prior bytes and the chosen bits within the current byte.The byte distribution is split into conditional bit costs for bitwise pruning.Source: B. Byte Priors and Bit Costs · p. 3
  • The eight bit costs sum to the completed byte’s negative log-probability, while α = 1 makes combined-metric ranking a maximum a posteriori rule.The language-model term is the payload’s negative log-prior, and the channel term is the path’s negative log-likelihood; α < 1 discounts the prior when it is overconfident.Source: B. Byte Priors and Bit Costs · p. 3

C. Decoding Procedure

Semantic SCL assigns language-model guidance at the byte level while updating and pruning branch metrics. After decoding, it selects a CRC-valid survivor when available.

C. Decoding Procedure

D. Threshold-Based LM Guidance

Threshold-based guidance uses provisional channel-only decoding to identify unreliable bytes for language-model assistance. Lower thresholds reduce language-model invocations and latency, with an error-rate trade-off.

D. Threshold-Based LM Guidance

  • Before each payload byte, the decoder saves its state and provisionally decodes the byte without new language-model costs, retaining previously accumulated costs.The best provisional survivor’s reliability is assessed from its payload-bit LLRs.Source: D. Threshold-Based LM Guidance · p. 3
  • When ρ_j < T, the decoder restores the pre-byte state and re-decodes with LM guidance; otherwise it keeps the provisional result.Restoration discards provisional updates so costs are accumulated only once.Source: D. Threshold-Based LM Guidance · p. 3
  • Lowering T reduces LM invocations and latency at the expense of error-rate performance; T = 0 gives CA-SCL and T = ∞ gives every-byte Semantic SCL.Source: D. Threshold-Based LM Guidance · p. 4

E. Language Model Adaptation

The authors fine-tune a ByT5 decoder for next-byte prediction on source-domain text. A worked example illustrates how bitwise language costs can change branch ranking during decoding.

E. Language Model Adaptation

  • The fine-tuning corpus contains 10,000 SNLI training sentences of 80–120 characters, split into 9,000 training and 1,000 validation sentences.Source: E. Language Model Adaptation · p. 4
  • The ByT5 decoder is fine-tuned with teacher forcing and next-byte negative log-likelihood, using AdamW with a 5 × 10^-5 learning rate and early stopping after two unimproved validation epochs.Training runs for up to ten epochs, with weight decay 0.01 and batch size 32.Source: E. Language Model Adaptation · p. 4
  • In the guided “g” example, bitwise language costs rank the correct branch first even though the channel cost alone favors the other branch.The figure marks bit costs that depart from g and boxes the smaller channel cost and smaller combined sum.Source: E. Language Model Adaptation · p. 4, Figure 2 · p. 4

IV. EXPERIMENTS

The experiments evaluate Semantic SCL on length-512 polar codes and select α=1 from validation results for subsequent tests. The evaluation uses SNLI text and compares against conventional CA-SCL under matched payloads and channel realizations.

A. Setup

  • Tests use N=512 at rates R=0.75 and R=0.5, with SNLI premise and hypothesis text truncated to 46 and 30 payload bytes, respectively.Sequences must be at least 80 bytes; the baseline is same-code, same-CRC CA-SCL.Source: A. Setup · p. 4
  • Compared decoders use identical payloads and channel realizations, with the polar reliability sequence specified for 5G NR and a 16-bit CRC.The pretrained ByT5-small model is fine-tuned using a single NVIDIA GeForce RTX 5090 GPU; the pipelines use Sionna.Source: A. Setup · pp. 4–5
  • α=1 achieves lower BLER than the other tested weights at every validation Eb/N0 and is fixed for test evaluations, without separate optimization by code rate or block length.The sweep uses N=512, R=0.75, L=8, and α ∈ {0, 0.5, 1, 2, 4}.Source: A. Setup · p. 5, Figure 3 · p. 5

B. BLER Analysis

Semantic SCL substantially reduces BLER at both evaluated code rates, including against conventional CA-SCL with much larger lists. The latency results show a trade-off: language-model guidance increases runtime at matched list sizes, while an L=8 Semantic SCL decoder is faster than CA-SCL with L=256.

B. BLER Analysis

  • At R=0.75 and L=16, BLER falls from 6.31 × 10^-1 to 3.68 × 10^-3 at Eb/N0=1.5 dB and from 3.37 × 10^-2 to 7.00 × 10^-5 at 2.5 dB.These comparisons are Semantic SCL versus conventional CA-SCL; Fig. 5 shows BLER for R=0.75.Source: B. BLER Analysis · p. 5, Figure 5 · p. 5
  • At R=0.5, L=16, and Eb/N0=1 dB, BLER falls from 1.01 × 10^-1 to 3.00 × 10^-4; L=4 Semantic SCL also beats CA-SCL L=256 through 1.5 dB.At R=0.75, L=4 Semantic SCL beats CA-SCL L=256 through 2.5 dB; Fig. 4 covers R=0.5.Source: B. BLER Analysis · p. 5, Figure 4 · p. 5

C. Latency

  • At matched list sizes, language-model guidance increases latency; for R=0.75, L=16 takes 29.682 ms versus 3.851 ms for CA-SCL.The reported timings are specific to the software implementation; CA-SCL with L≥256 uses batch size 4 while other configurations use batch size 64.Source: C. Latency · p. 5, Table I · p. 6
  • Semantic SCL L=8 beats CA-SCL L=256 in BLER while taking 8.178 versus 55.689 ms at R=0.5 and 16.291 versus 61.951 ms at R=0.75.The authors conclude that language-model computation can partly replace the cost of maintaining much larger SCL lists.Source: C. Latency · p. 5

D. Threshold-based Semantic SCL

Threshold-based replay trades BLER for latency, while the conclusion reports BLER gains over CA-SCL and a faster comparison against a larger-list decoder.

D. Threshold-based Semantic SCL

V. CONCLUSION

  • For N=512 and R=0.75, Semantic SCL cuts BLER about 171-fold versus CA-SCL with L=16 at Eb/N0=1.5 dB; with L=8, it beats CA-SCL with L=256 at about one-quarter the decoding time.Source: §V · p. 6
  • Guiding only bytes with unreliable channel LLRs reduces decoding time about two thirds, at a loss of about 0.2 dB.Source: §V · p. 6

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